<PAGE>   1
                                  SCHEDULE 14A
                                 (RULE 14a-101)

                    INFORMATION REQUIRED IN PROXY STATEMENT

                            SCHEDULE 14a INFORMATION
 
          PROXY STATEMENT PURSUANT TO SECTION 14(a) OF THE SECURITIES
                    EXCHANGE ACT OF 1934 (AMENDMENT NO.   )
 
Filed by the Registrant [X]
 
Filed by a Party other than the Registrant [ ]
 
Check the appropriate box:
 
[ ]  Preliminary Proxy Statement          [ ]  Confidential, for Use of the 
                                               Commission Only (as permitted by 
                                               Rule 14a-6(e)(2))
[X]  Definitive Proxy Statement
[ ]  Definitive Additional Materials
[ ]  Soliciting Material Pursuant to Rule 14a-11(c) or Rule 14a-12
 
                                BESTWAY, INC.
--------------------------------------------------------------------------------
                (Name of Registrant as Specified in Its Charter)


--------------------------------------------------------------------------------
   (Name of Person(s) Filing Proxy Statement, if Other Than the Registrant)
 
Payment of Filing Fee (Check the appropriate box):
 
   [X]  No fee required.

   [ ]  Fee computed on table below per Exchange Act Rules 14a-6(i)(1) and 0-11.

   (1)  Title of each class of securities to which transaction applies:

        -----------------------------------------------------------------------

   (2)  Aggregate number of securities to which transaction applies:

        -----------------------------------------------------------------------

   (3)  Per unit price or other underlying value of transaction computed
        pursuant to Exchange Act Rule 0-11 (Set forth the amount on which the
        filing fee is calculated and state how it was determined):

        -----------------------------------------------------------------------

   (4)  Proposed maximum aggregate value of transaction:

        -----------------------------------------------------------------------

   (5)  Total fee paid:

        -----------------------------------------------------------------------

   [ ]  Fee paid previously with preliminary materials.

   [ ]  Check box if any part of the fee is offset as provided by Exchange Act
   Rule 0-11(a)(2) and identify the filing for which the offsetting fee was 
   paid previously. Identify the previous filing by registration statement 
   number, or the form or Schedule and the date of its filing.

   (1)  Amount Previously Paid:

        -----------------------------------------------------------------------

   (2)  Form, Schedule or Registration Statement No.:

        -----------------------------------------------------------------------

   (3)  Filing Party:

        -----------------------------------------------------------------------

   (4)  Date Filed:

        -----------------------------------------------------------------------
<PAGE>   2
                                  BESTWAY, INC.
                           7800 N. STEMMONS, SUITE 320
                                DALLAS, TX 75247

                          -----------------------------

                    NOTICE OF ANNUAL MEETING OF STOCKHOLDERS
                             TO BE HELD JULY 3, 1998

                          -----------------------------

TO THE STOCKHOLDERS OF
BESTWAY, INC.

         NOTICE IS HEREBY GIVEN that the Annual Meeting of Stockholders of
Bestway, Inc., a Delaware corporation (the "Company"), will be held at 9:00
a.m., Central Daylight Time, at the corporate office, 7800 N. Stemmons, Suite
320, Dallas, TX on Friday, July 3, 1998 for the following purposes:

         1. To elect three (3) Directors of the Company, each to serve until the
next annual meeting of stockholders and until his successor has been duly
elected and qualified; and

         2. To consider and act upon the ratification of the appointment of
Coopers & Lybrand L.L.P. as the Company's independent public accountants for the
1998 fiscal year; and

         3. To transact such other business as may properly come before the
meeting or any adjournment(s) thereof.

         Management is not aware of any other matters that will come before the
meeting.

         The Board of Directors has fixed the close of business on Tuesday, June
2, 1998 as the Record Date for the determination of stockholders entitled to
notice of and vote at this meeting and any adjournment thereof, and only
stockholders of record at such time will be so entitled to vote.

         IT IS IMPORTANT THAT YOUR STOCK BE REPRESENTED AT THE MEETING
REGARDLESS OF THE NUMBER OF SHARES YOU HOLD. PLEASE COMPLETE, SIGN AND MAIL THE
ENCLOSED PROXY IN THE ACCOMPANYING ENVELOPE PROMPTLY, WHETHER OR NOT YOU INTEND
TO BE PRESENT AT THE MEETING. THE PROXY IS REVOCABLE AT ANY TIME PRIOR TO ITS
EXERCISE.


                                      By Order of the Board of Directors,



                                      /s/ Beth A. Durrett
                                      -----------------------------------
                                      Beth A. Durrett
                                      Secretary



June 11, 1998
Dallas, Texas


<PAGE>   3

                                 PROXY STATEMENT
                                  BESTWAY, INC.
                     --------------------------------------

                         ANNUAL MEETING OF STOCKHOLDERS
                                  JULY 3, 1998

                     --------------------------------------

                                  INTRODUCTION

         The accompanying Proxy is being solicited by the Board of Directors of
Bestway, Inc. (the "Company") on behalf of the Company for use at the Annual
Meeting of Stockholders to be held at the corporate office, 7800 N. Stemmons,
Suite 320, Dallas, Texas on Friday, July 3, 1998 at 9:00 a.m., Central Daylight
Time and at any adjournment thereof. The approximate date of which the Proxy
Statement and the form of Proxy are being sent to stockholders is June 11, 1998.
The cost of preparing and mailing the enclosed material is to be borne by the
Company.

         Proxies in the accompanying form which are properly executed and duly
returned to the Company will be voted in accordance with the instructions
contained therein. If no instruction is given with respect to any proposal to be
acted upon, the proxy will be voted in favor of the proposals set forth therein.
Each proxy granted may be revoked at any time prior to its exercise by the
subsequent execution and submission of a revised proxy, by written notice to the
Secretary of the Company, or by voting in person at the meeting.

         Votes cast by proxy or in person at the Annual Meeting will be counted
by the persons appointed by the Company to act as election inspectors for the
meeting. The election inspectors will treat shares represented by proxies that
reflect abstentions as shares that are present and entitled to vote, for
purposes of determining the presence of a quorum and for purposes of determining
the outcome of any matter submitted to the shareholders for a vote. Abstentions,
however, do not constitute a vote "for" or "against" any matter and thus will be
disregarded in the calculation of a plurality or of "votes cast".

         The election inspectors will treat shares referred to as "broker
non-votes" (i.e., shares held by brokers or nominees as to which instructions
have not been received from the beneficial owners or persons entitled to vote
that the broker or nominee does not have discretionary power to vote on a
particular matter) as shares that are present and entitled to vote for purposes
of determining the presence of a quorum. However, for purposes of determining
the outcome of any matter as to which the broker has physically indicated on the
proxy that it does not have discretionary authority to vote, those shares will
be treated as not present and entitled to vote with respect to that matter (even
though those shares are considered entitled to vote for quorum purposes and may
be entitled to vote on other matters).

         In the election of directors ("Directors") to the Board of Directors,
shares present by not voting will be disregarded (except for quorum purposes)
and the candidates for the election receiving the highest number of affirmative
votes of the shares entitled to be voted for them, up to the number of Directors
to be elected by those shares, will be elected and votes cast against a
candidate or votes withheld will have no legal effect.



<PAGE>   4



                       VOTING SECURITIES AND VOTE REQUIRED

         The only class of voting securities of the Company is its Common Stock,
par value $.01 per share (the "Common Stock"), each share of which entitles the
holder thereof to one vote. As of June 2, 1998, there were 1,751,092 shares of
the Company's Common Stock outstanding and entitled to vote at the meeting or
any adjournment thereof. Assuming the presence of a quorum, the affirmative vote
of a majority of the shares of Common Stock represented and entitled to vote at
the Annual Meeting of Stockholders is required for the adoption of the proposals
set forth herein except for the election of Directors (Proposal No. 1), in which
nominees will be elected by a plurality of the votes of the shares present in
person or by proxy and entitled to vote on the election of Directors.

                     OWNERSHIP OF BESTWAY, INC. COMMON STOCK

         The following table sets forth certain information as of April 30,
1998, obtained from information furnished by the persons named below, concerning
the beneficial stock ownership of each person known to the Company who may be
deemed to be the beneficial owner of more than five percent of the Company's
Common Stock, each Director of the Company and all Directors and executive
officers of the Company as a group. The Company has no other class of equity
securities outstanding other then its Common Stock.

<TABLE>
<CAPTION>
NAME AND ADDRESS                              NUMBER OF SHARES OF COMMON         PERCENT
OF BENEFICIAL OWNER                           STOCK BENEFICIALLY OWNED(1)       OF CLASS
-------------------                           ---------------------------       --------
<S>                                                 <C>                           <C>
O'Donnell & Masur, L.P. ("O&M")                        981,872                    56.2%
5949 Sherry Lane, Suite 1450
Dallas, Texas  75225

James A. O'Donnell(2)                                  983,872                    56.3%
5949 Sherry Lane, Suite 1450
Dallas, Texas  75225

Mark Masur(3)                                          981,952                    56.2%
5949 Sherry Lane, Suite 1450
Dallas, Texas  75225

R. Brooks Reed(4)                                       58,873                     3.4%
7800 Stemmons, Suite 320
Dallas, Texas  75247

Jack E. Meyer                                           16,203                      .9%
7800 Stemmons, Suite 320
Dallas, Texas  75247

All Directors and executive officers                 1,088,103                    62.2%
as a group (6 persons)

Robert D. Simons                                        92,517                     5.3%
317 Coinbow Drive
Mt. Pleasant, South Carolina  29464
</TABLE>


<PAGE>   5


(1)      Except as noted, beneficial ownership consists of sole voting and
         investment power. The inclusion of shares that may be deemed
         beneficially owned herein, however, does not constitute an admission
         that the named stockholders are direct or indirect beneficial owners of
         such shares.

(2)      Mr. O'Donnell has sole voting power and sole investment power with
         respect to 2,000 shares of Common Stock of the Company that he owns
         directly. Mr. O'Donnell by virtue of his being a general partner of O&M
         may be deemed, for purposes of determining beneficial ownership
         pursuant to Rule 13d-3, to own beneficially the 981,872 shares of
         Common Stock owned by O&M.

(3)      Mr. Masur has sole voting power and sole investment power with respect
         to 80 shares of Common Stock of the Company that he owns directly. Mr.
         Masur by virtue of his being a general partner of O&M may be deemed,
         for purposes of determining beneficial ownership pursuant to Rule
         13d-3, to own beneficially the 981,872 shares of Common Stock owned by
         O&M.

(4)      Excludes a total of 71,000 shares of Common Stock of the Company owned
         by Mr. Reed's spouse and adult children which Mr. Reed may be deemed
         beneficially to own.


                              ELECTION OF DIRECTORS
                                (PROPOSAL NO. 1)

         The By-laws of the Company provide that the number of Directors which
shall constitute the whole Board shall be fixed and determined from time to time
by resolution adopted by the Board of Directors. This year three (3) persons
will comprise the Board and will be elected. Each Director will serve until the
next annual meeting of stockholders and until his successor has been elected and
qualified. The election of Directors requires a plurality of the votes cast at
the meeting.

         THE BOARD OF DIRECTORS RECOMMENDS THAT THE STOCKHOLDERS VOTE FOR THE
ELECTION OF THE DIRECTOR NOMINEES.

         It is intended that the shares represented by properly executed proxies
will be voted for the election of the persons listed below except where
authority to so vote is withheld. The nominees have indicated that they are
willing to serve as Directors, and management of the Company does not
contemplate that any of the nominees will be unable to serve as a Director or
become unavailable for any reason, but if that should occur before the meeting,
such proxy will be voted for another nominee or nominees to be selected by
management.

         The nominees for Director, all of whom are now serving as Directors of
the Company are listed below together with biographical information as to (i)
the name and age of each nominee, (ii) the position and offices with the Company
of each nominee, (iii) the year during which each nominee first became a
Director of the Company, and (iv) the principal occupation or employment of such
nominee for at least the past five years. Also listed below are executive
officers of the Company.


<PAGE>   6



<TABLE>
<CAPTION>
      Name               Age                   Position
      ----               ---                   --------
<S>                      <C>      <C>
Jack E. Meyer            54       Director and Member of the Audit Committee of the Board of Directors
James A. O'Donnell       45       Director and Member of the Audit Committee of the Board of Directors
R. Brooks Reed           56       Chairman of the Board and Chief Executive Officer
Teresa A. Sheffield      37       President and Chief Operating Officer
Beth A. Durrett          40       Senior Vice President - Finance and Secretary
Joe R. McElroy           40       Vice President - Real Estate
</TABLE>


         Mr. Meyer has served as a director of the Company since 1980. Mr. Meyer
is currently President and Chief Executive Officer of Urologix, Inc. From March
1993 to January 1994 he was President and Chief Executive Officer for Fiberoptic
Sensor Technologies. Mr. Meyer has served as a director for Urologix, Inc. since
1994.

         Mr. O'Donnell has served as a director of the Company since 1987. Mr.
O'Donnell is currently a partner with the private equity firm of Cravey, Green &
Wahlen and since 1987 has been a general partner of O'Donnell and Masur, L.P., a
venture capital investment firm which is a significant stockholder and debt
holder of the Company.

         Mr. Reed has served as Chairman of the Board of Directors and Chief
Executive Officer of the Company since 1979. From 1983 to May 1997, Mr. Reed
served as President of the Company. Mr. Reed is also a principal of Phoenix
Partners, Inc., a private investment company engaged in the acquisition and
operation of medium-sized businesses in a variety of industries.

         Ms. Sheffield has served as President and Chief Operating Officer since
May 1997. From July 1992 to May 1997, Ms. Sheffield served as Vice President -
Operations. From February 1988 to July 1992, Ms. Sheffield served in various
capacities with the Company.

         Ms. Durrett has served as Senior Vice President - Finance of the
Company since May 1997. From 1987 to May 1997, Ms. Durrett served as Vice
President - Controller and was appointed Secretary in 1991. Ms. Durrett has
served in various capacities with the Company since September 1979.

         Mr. McElroy has served as Vice President - Real Estate since May 1997.
From January 1996 to May 1997, Mr. McElroy served as Director - Real Estate.
Prior to joining the Company, Mr. McElroy was Director of Real Estate for
Drinkard Development, Inc.

BOARD OF DIRECTORS MEETINGS, COMMITTEES AND FEES

         The Board of Directors held one regular meeting during the fiscal year
ended July 31, 1997 and acted two times by unanimous consent. No Director
attended fewer than 75% of the meetings of the Board of Directors or committees
thereof from August 1, 1996 to July 31, 1997.

         The Board of Directors has a two member Audit Committee which held one
meeting during the fiscal year ended July 31, 1997. The Audit Committee, neither
member of which is an 



<PAGE>   7

officer of the Company, is responsible for (a) nominating the independent
auditors for the annual audit, (b) reviewing the plan for the audit and related
services and reviewing audit results and annual financial statements, (c)
overseeing the adequacy of the Company's system of internal accounting controls
and compliance with the Foreign Corrupt Practices Act, and (d) overseeing
compliance with Securities and Exchange Commission requirements of disclosure of
Audit Committee activities. The present members of the Audit Committee, none of
whom is otherwise employed by the Company, are Jack E. Meyer and James A.
O'Donnell.

                 CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS

         The Company is indebted to O&M in the principal amount of $3,000,000.
One of the Company's Directors, James A. O'Donnell, is a general principal in
O&M.

                             EXECUTIVE COMPENSATION

         The following Summary Compensation Table shows all cash and other
compensation paid (or to be paid) by the Company for the fiscal years ended July
31, 1997, 1996 and 1995 to the Company's Chief Executive Officer and highest
compensated executive officer for services rendered in all capacities in which
they served during each period whose total annual salary and bonus exceeded
$100,000 in the fiscal year ended July 31, 1997.

<TABLE>
<CAPTION>
                                                                                                     Long-Term
                                                                                                    Compensation
                                                                        Annual Compensation             Awards
                                                                  ------------------------------    ------------
                                                                                                     Restricted
                     Name and                         Fiscal         Salary           Bonus             Stock
                Principal Position                     Year           ($)              ($)           Awards ($)
                ------------------                     ----           ---              ---           ----------
<S>                                                    <C>          <C>               <C>              <C>
R. Brooks Reed, Chairman and Chief Executive           1997         $150,000               --             --
Officer                                                1996         $150,000               --             --
                                                       1995         $150,000          $37,111(1)          --

Teresa A. Sheffield                                    1997         $116,307          $19,542             --
President and Chief Operating Officer                  1996          $85,346          $30,376             --
                                                       1995          $71,615          $29,327             --
</TABLE>


(1)      This amount represents the tax liability paid by the Company relating
         to the restricted stock awarded by the Company to Mr. Reed in 1993 in
         the amount of 109,658 shares of the Company's Common Stock in
         connection with the restructuring of the Company.



<PAGE>   8




                               OPTION GRANTS TABLE

         The following table shows all options granted by the Company for the
fiscal year ended July 31, 1997 to the Company's highest compensated executive
officers listed above: (i) the number of shares covered by such options; (ii)
the percent that such options represented of total options granted to all the
Company's employees during the 1997 fiscal year; (iii) the exercise price, and
(iv) the expiration date.

<TABLE>
<CAPTION>
                                                      Percent of Total
                                                     Options Granted to        Exercise
                                                     Employees in 1997        Price Per           Expiration
          Name                Options Granted           Fiscal Year             Share                Date
          ----                ---------------        ------------------       ---------           ----------
<S>                                <C>                       <C>                  <C>                <C>
R. Brooks Reed                     --                        --                   --                 --
Teresa A. Sheffield                --                        --                   --                 --
</TABLE>


AGGREGATED OPTION EXERCISES IN LAST FISCAL YEAR AND FISCAL YEAR END OPTION
VALUES

         The following table shows for the fiscal year ended July 31, 1997 to
the Company's highest compensated executive officers listed above: (i) the
number of shares of the Company's Common Stock acquired upon exercise of options
during fiscal year 1997; (ii) the aggregate dollar value realized upon exercise;
(iii) the total number of unexercised options held at the end of fiscal year
1997; and (iv) the aggregate dollar value of in-the-money unexercised options
held at the end of fiscal year 1997.

<TABLE>
<CAPTION>
                                                       Number of Unexercised            Value of Unexercised
                             Shares       Value        Options at 1997 Fiscal          In-the-Money Options at
                                                            Year End                  1997 Fiscal Year End (2)
                          Acquired on    Realized  -----------------------------     ----------------------------
         Name             Exercise (#)     ($)     Exercisable     Unexercisable     Exercisable    Unexercisable
         ----             ------------     ---     -----------     -------------     -----------    -------------
<S>                          <C>           <C>        <C>             <C>             <C>              <C>
R. Brooks Reed               --            --             --              --               --               --
Teresa A. Sheffield          --            --         30,400          30,400          $45,600          $45,600
</TABLE>


(2) Market value of underlying securities at year-end minus the exercise price.

RETIREMENT SAVINGS PLAN PROGRAM - 401(k) PLAN

         The Company established a Retirement Savings Plan (the "Savings Plan")
effective as of September 1, 1994 which is intended to qualify under Section
401(k) of the Internal Revenue Code of 1986 (the "Code"). Employees who have
been employed with the Company for one year or more are eligible for
participation in the Savings Plan. Pursuant to the Savings Plan, employees may
elect to reduce their current compensation by up to 15% (subject to certain
limitations under the Code) and have the amount of such reduction contributed to
the Savings Plan. The Savings Plan permits, but does not require, additional or
matching contributions to the Savings Plan by the Company on behalf of all
participants in the Savings Plan. The Company has made no additional or matching
contributions to the Savings Plan. The Board of Directors of the Company intends
to conduct a review at the end of each fiscal year to determine whether the
Company will make any additional or matching contributions to the Savings Plan.
All assets of the Savings Plan are held in trust at all times.


<PAGE>   9


COMPENSATION OF DIRECTORS

         The Company's policy is to reimburse its directors for travel, lodging
and related expenses incurred on account of attendance at meetings of the Board
of Directors and committees thereof. For their participation in special meetings
of the Board convened by conference telephone call, for services in relation to
any matters adopted by the unanimous written consent of the directors, and for
all the various services rendered, directors, other than those who are employees
or consultants of the Company, receive an annual retainer of $1,200.
Additionally, each director, other than those who are officers or employees of
the Company, receive $500 for each meeting attended. In order to conserve cash,
no fees have been paid in cash to any director since 1988 and from 1984 through
1988, directors received Common Stock of the Company in lieu of fees.
Furthermore, in connection with the 1993 restructuring of the Company, Messrs.
R. Brooks Reed and Jack E. Meyer received 109,658 and 13,271 shares,
respectively, of the Company's Common Stock. The purpose of granting stock to
Messrs. Reed and Meyer was to prevent dilution of their respective ownership
positions in the Company, to provide an incentive to them to build stockholder
value following the restructuring and to compensate them for past service to the
Company, including, but no limited to, their waiver of directors fees and
service as directors without compensation since 1988.

COMPENSATION COMMITTEE INTERLOCKS AND INSIDER PARTICIPATION

         Decisions regarding the compensation of the executive officers of the
Company are made by the Board of Directors. In fiscal year 1997, decisions
concerning the compensation of Ms. Beth A. Durrett, Mr. Joe R. McElroy and Ms.
Teresa A. Sheffield were made by the entire Board of Directors and decisions
concerning the compensation of Mr. R. Brooks Reed were made by Mr. Jack E. Meyer
and Mr. James A. O'Donnell.

                   PROPOSAL TO RATIFY COOPERS & LYBRAND L.L.P
             AS INDEPENDENT PUBLIC ACCOUNTANTS FOR FISCAL YEAR 1998
                                (PROPOSAL NO. 2)

         The Board of Directors has appointed Coopers & Lybrand L.L.P.,
independent certified public accountants, to examine and report on the Company's
financial statements for the fiscal year ended July 31, 1998. The firm has
served as the Company's independent accountants since 1976. It is expected that
a representative of such firm will be in attendance at the Company's Annual
Meeting of Stockholders and will be afforded an opportunity to make a statement
at the meeting if he so desires and will be available to respond to appropriate
questions. Audit services included examination of the Company's filings with the
Securities and Exchange Commission and consultation in connection with various
audit-related accounting matters.


<PAGE>   10



THE STOCKHOLDERS ARE REQUESTED BY THE BOARD OF DIRECTORS TO VOTE FOR THE
APPROVAL OF THE APPOINTMENT OF COOPERS AND LYBRAND L.L.P. AS THE COMPANY'S
INDEPENDENT PUBLIC ACCOUNTANTS FOR THE FISCAL YEAR ENDING JULY 31, 1998.

                        PROPOSAL FOR NEXT ANNUAL MEETING

         Any proposal of holders of Common Stock intended to be presented at the
Annual Meeting of Stockholders of the Company to be held in 1999 must be
received by the Company at 7800 N. Stemmons, Suite 320, Dallas, Texas 75247, no
later than September 15, 1998, in order to be included in the Proxy Statement
and Form of Proxy relating to that meeting.

                                     GENERAL

         The cost of preparing and mailing the enclosed material is to be borne
by the Company. In addition to the solicitation of proxies by mail, certain
officers, Directors and regular employees of the Company may, without additional
compensation, solicit proxies on behalf of management by telephone, telegraph or
personal interview. The cost of any solicitation will be borne by the Company.
Upon request, persons, including brokers, holding shares for others will be
reimbursed for their expenses in transmitting proxy material to their principals
and in seeking instructions by mail, telephone or telegraph for their
principals.

         Management does not intend to bring any matters before the meeting
other than those mentioned above and is not aware of any other matters to be
presented before the meeting. However, if any other matters should be presented
properly to the meeting, it is intended that the persons named in the enclosed
proxy will vote such proxy in accordance with their best judgment. A copy of the
Company's Annual Report is being mailed to the stockholders with this Proxy
Statement. The Company's Annual Report to stockholders contains financial
statements for the periods ended July 31, 1997, July 31, 1996 and July 31, 1995
which are incorporated by reference herein. A COPY OF THE COMPANY'S ANNUAL
REPORT ON FORM 10-K FILED WITH THE SECURITIES AND EXCHANGE COMMISSION IS
AVAILABLE TO EACH STOCKHOLDER WITHOUT CHARGE. ANY STOCKHOLDER DESIRING A COPY OF
THE ANNUAL REPORT ON FORM 10-K SHOULD ADDRESS HIS REQUEST TO MS. BETH A.
DURRETT, SECRETARY, 7800 N. STEMMONS, SUITE 320, DALLAS, TEXAS, 75247.



                                   By Order of the Board of Directors,


                                   /s/ Beth A. Durrett
                                   -----------------------------------
                                   Beth A. Durrett
                                   Secretary

June 11, 1998
Dallas, Texas

<PAGE>   11


                                  BESTWAY, INC.
               PROXY SOLICITED OF BEHALF OF THE BOARD OF DIRECTORS

The undersigned hereby appoints R. Brooks Reed and Beth A. Durrett, and each of
them, with full power of substitution, to vote as indicated below, and act with
respect to all shares of Common Stock of Bestway, Inc., (the "Company") standing
in the name of the undersigned, at the annual meeting of stockholders to be held
at 9:00 a.m. on Friday, July 3, 1998, in the Company's corporate office at 7800
N. Stemmons Freeway, Suite 320, Dallas, Texas, or at any adjournment thereof,
with all the power the undersigned would possess if personally present:

1.   Election of the following nominees as Directors:  

     R. Brooks Reed, Jack E. Meyer and James A. O'Donnell.
     
     FOR all of the nominees                 WITHOUT AUTHORITY to vote 
     (except as otherwise market             for all nominees
     below)                                  


     INSTRUCTIONS: To withhold authority to vote for any particular nominee,
     write such person's name in the following space.


--------------------------------------------------------------------------------

2.   Ratification of the appointment of Coopers & Lybrand L.L.P. as the
     Company's independent public accountants for the fiscal year 1998.

               FOR            AGAINST             ABSTAIN

3.   In their discretion, the proxies are authorized to vote upon such other
     business as may properly come before the meeting or any adjournment(s)
     thereof.

THIS PROXY WHEN PROPERLY EXECUTED WILL BE VOTED IN THE MANNER DIRECTED ABOVE. IF
NO DIRECTION IS MADE, THE PROXY WILL BE VOTED FOR PROPOSAL 1, 2 AND 3.


<PAGE>   12



IMPORTANT: To ensure a quorum and to avoid the expense and delay of sending
follow-up letters, please mark, sign, date and mail this proxy in the
accompanying envelop.




                                    Date:                                , 1998
                                         --------------------------------

                                    -------------------------------------------

                                    -------------------------------------------


                                    Please sign exactly as name appears hereon.
                                    For a joint account, each owner should sign.
                                    Persons signing as attorney, executor,
                                    administrator, trustee or guardian or in any
                                    other representative capacity should
                                    indicate their full title. If a corporation,
                                    please sign in full corporate name by
                                    president or other authorized officer. If a
                                    partnership, please sign in partnership name
                                    by authorized person.