<PAGE>   1
                                                                     EXHIBIT 4.1


                             LETTER OF TRANSMITTAL
                              with respect to the
                            Exchange of Common Stock
                                       of
                              BARGO ENERGY COMPANY
                           For Shares of Common Stock
                                       of
                         MISSION RESOURCES CORPORATION



     Mail or deliver this Letter of Transmittal, or a facsimile hereof, together
with the certificates representing your shares to American Stock Transfer and
Trust Company, the Exchange Agent, at the following addresses:

<TABLE>
<CAPTION>

           By Hand:                           By First Class Mail:                   By Overnight Carrier or
                                                                                         Certified Mail:
<S>                                     <C>                                      <C>
  6201 15th Ave., Third Floor             6201 15th Ave., Third Floor              6201 15th Ave., Third Floor
      Brooklyn, NY 11219                      Brooklyn, NY 11219                       Brooklyn, NY 11219
Attn: Reorganization Department         Attn: Reorganization Department          Attn: Reorganization Department
</TABLE>


     For information, contact American Stock Transfer and Trust Company at
1-800-937-5449.


                       DESCRIPTION OF SHARES SURRENDERED

<TABLE>
<CAPTION>
                            (1)                                                 (2)                           (3)
                                                                      CERTIFICATE NUMBER(S)
        NAME AND ADDRESS(ES) OF REGISTERED HOLDER(S)                 (ATTACH ADDITIONAL LIST           NUMBER OF SHARES
(PLEASE FILL IN EXACTLY AS NAME(S) APPEAR ON CERTIFICATE(S))              IF NECESSARY)             DELIVERED FOR EXCHANGE
------------------------------------------------------------         -----------------------        ----------------------
<S>                                                                  <C>                            <C>
                                                                     -----------------------        ----------------------

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

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

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

                                                                     -----------------------        ----------------------
                                                                           Total Shares
------------------------------------------------------------         -----------------------        ----------------------
</TABLE>

Please issue one certificate for the shares of Mission Common Stock to which the
undersigned is entitled in the name of the undersigned shown above (unless a
different name is indicated in the Special Issuance Instructions box below),
for delivery by mail to the address shown above (unless a different address is
indicated in the Special Delivery Instructions box or the Special Issuance
Instructions box below).

<PAGE>   2
Ladies and Gentlemen:

         In connection with the merger (the "MERGER") of Bargo Energy Company, a
Texas corporation ("BARGO"), with and into Bellwether Exploration Company, a
Delaware corporation ("BELLWETHER"), which, at the effective time of the merger
(the "EFFECTIVE TIME"), will be renamed Mission Resources Corporation ("MISSION
RESOURCES"), and pursuant to the Agreement and Plan of Merger dated January 24,
2001 (the "MERGER AGREEMENT"), as described in the joint proxy
statement/prospectus/annual report of Bargo and Bellwether dated April 24,
2001 (the "PROSPECTUS"), the undersigned hereby surrenders the number of shares
of common stock of Bargo, par value $0.01 per share ("BARGO COMMON STOCK"),
represented by the certificate(s) described above (the "CERTIFICATES"), in
exchange for $0.45 in cash (the "CASH CONSIDERATION") and 0.0958 shares of
Mission common stock, par value $0.01 per share ("MISSION COMMON STOCK"), for
each share of Bargo Common Stock tendered hereby. Undefined capitalized terms
herein are defined in the Merger Agreement.

         All authority herein conferred or agreed to be conferred shall survive
the death or incapacity of the undersigned, and any obligation of the
undersigned hereunder shall be binding upon the heirs, personal representatives,
estates, successors and assigns of the undersigned. The undersigned hereby
represents and warrants that the undersigned is the owner of the shares of Bargo
Common Stock delivered hereby and has full power and authority to submit and
exchange the shares of Bargo Common Stock delivered for exchange hereby. The
undersigned will, upon request, execute and deliver any additional documents
deemed by the Exchange Agent or Mission Resources to be necessary or desirable
to complete the exchange of the shares of Bargo Common Stock tendered for
exchange hereby.

         The undersigned hereby irrevocably constitutes and appoints the
Exchange Agent the true and lawful attorney-in-fact of the undersigned with
respect to the Certificates with full power of substitution (such power of
attorney being deemed to be an irrevocable power coupled with an interest) to
deliver such Certificates on the account books maintained by and to deliver as
the undersigned's agent the shares of Mission Common Stock to which the
undersigned is entitled upon the surrender of the Certificates.

         The undersigned understands and agrees that the method of delivery of
the shares of Bargo Common Stock and this Letter of Transmittal is at the
election and risk of the holder of the shares of Bargo Common Stock. If delivery
of the shares of Bargo Common Stock is by mail, registered mail with return
receipt requested, properly insured, is recommended. Neither this Letter of
Transmittal nor any shares of Bargo Common Stock should be sent to Mission
Resources.

         The undersigned hereby acknowledges that the undersigned has read the
Instructions accompanying this Letter of Transmittal.


<PAGE>   3
--------------------------------------------------------------------------------

                          SPECIAL ISSUANCE INSTRUCTIONS
                          (See Instructions 2, 4 and 6)


(To be completed only if the certificates for shares of Mission Common Stock and
the Cash Consideration are to be issued in the name of someone other than the
undersigned.)


Issue and mail shares of Mission Common Stock to:

    Name:
         ------------------------------------------------------------
                                (Please Print)

    Address:
            ---------------------------------------------------------


    -----------------------------------------------------------------
    (City)                          (State)                     (ZIP)


                         (COMPLETE SUBSTITUTE FORM W-9)

                   (Tax Identification or Social Security No.)

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





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

                          SPECIAL DELIVERY INSTRUCTIONS
                          (See Instructions 2, 4 and 6)


(To be completed only if the certificates for shares of Mission Common Stock and
the Cash Consideration are to be mailed to the undersigned at an address other
than that shown on the record address.)


Mail shares of Mission Common Stock to:

    Name:
         ------------------------------------------------------------
                                (Please Print)

    Address:
            ---------------------------------------------------------


    -----------------------------------------------------------------
    (City)                          (State)                     (ZIP)


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




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

BY EXECUTING THIS LETTER OF TRANSMITTAL, THE UNDERSIGNED HEREBY DELIVERS TO
MISSION RESOURCES FOR EXCHANGE THE SECURITIES INDICATED IN THE BOX ENTITLED
"DESCRIPTION OF SHARES SURRENDERED."

                                   SIGN HERE
                              (See Instruction 4)
                         (Complete Substitute Form W-9)

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

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

    -----------------------------------------------------------------
                       (Signature(s) of Holder(s))

    Dated:                                                , 2001
          ------------------------------------------------

    Name:
         ------------------------------------------------------------
                                (Please Print)

         ------------------------------------------------------------
           (Title of signer if acting in a representative capacity)

    Address:
            ---------------------------------------------------------


    -----------------------------------------------------------------
    (City)                          (State)                     (ZIP)

Telephone Number
                -----------------------------------------------------

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




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

                          SIGNATURE(S) GUARANTEED BY:

                      (To be completed only if required by
                             Instructions 2 and 4)

The undersigned hereby guarantees the signature(s) which appear(s) on this
Letter of Transmittal and the Certificates and any stock powers surrendered
pursuant to this Letter of Transmittal.


    -----------------------------------------------------------------
                 (Name of Institution Issuing Guarantee)

    By:
       --------------------------------------------------------------
                           (Authorized Signature)

    Title:
          -----------------------------------------------------------

    Address of Guaranteeing Firm:
                                 ------------------------------------

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

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

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

--------------------------------------------------------------------------------
<PAGE>   4

                                  INSTRUCTIONS

     FORMING PART OF THE TERMS AND CONDITIONS OF THIS LETTER OF TRANSMITTAL

         1. Use of Letter of Transmittal. This Letter of Transmittal, properly
completed and duly executed, together with the surrendered Certificates and any
documents required by this Letter of Transmittal, should be sent by mail or
overnight courier or delivered by hand to the Exchange Agent, in each case at
the appropriate address set forth on the front page of this Letter of
Transmittal, in order to make an effective surrender. Until all necessary steps
have been taken to surrender Certificates, no exchange shall be made. The method
of delivery of all documents is at the option and risk of the undersigned and
the delivery will be deemed made only when actually received. If delivery is by
mail, registered mail with return receipt requested, properly insured, is
recommended. A return envelope is enclosed for your convenience.

         2. Guarantee of Signatures. Signatures on this Letter of Transmittal
must be guaranteed in accordance with Rule 17Ad-15 (promulgated under the
Securities Exchange Act of 1934) by an eligible guarantor institution which is a
participant in a stock transfer association recognized program, such as a firm
that is a member of a registered national securities exchange, a member of the
National Association of Securities Dealers, Inc., by a commercial bank or trust
company having an office or correspondent in the United States or by an
international bank, securities dealer, securities broker or other financial
institution licensed to do business in its home country (an "ELIGIBLE
INSTITUTION") unless (i) the Letter of Transmittal is signed by the registered
holder(s) of the shares of Bargo Common Stock tendered therewith and such
holder(s) have not completed the "Special Issuance Instructions" or "Special
Delivery Instructions" above or (ii) the shares of Bargo Common Stock described
above are delivered for the account of an Eligible Institution. IN ALL OTHER
CASES ALL SIGNATURES MUST BE GUARANTEED BY AN ELIGIBLE INSTITUTION.

         3. Inadequate Space. If the space provided in the box entitled
"Description of Shares Surrendered" above is inadequate, the certificate numbers
and number of shares of Bargo Common Stock being delivered should be listed on a
separate signed schedule affixed hereto.

         4. Signatures on this Letter of Transmittal, Powers of Attorney and
Endorsements.

          (a)  If this Letter of Transmittal is signed by the registered
               holder(s) of the shares of Bargo Common Stock delivered herewith,
               the signature(s) of the holder on this Letter of Transmittal must
               correspond exactly with the name(s) as written on the face of the
               Certificate without alteration, or any change whatsoever.

          (b)  If any shares of Bargo Common Stock are owned of record by two or
               more joint owners, all such owners must sign this Letter of
               Transmittal.

          (c)  If any shares of Bargo Common Stock are registered in different
               names on different Certificates, it will be necessary to
               complete, sign and submit as many separate copies of this Letter
               of Transmittal and any necessary or required documents as there
               are different registrations of Certificates.


<PAGE>   5


          (d)  Do not endorse the Certificates if the Mission Common Stock
               certificate is to be issued in the name of the registered
               holder(s) unless the registered holder(s) is/are completing the
               Special Issuance Instructions.

          (e)  If the certificates of the Mission Common Stock and the Cash
               Consideration are to be issued and paid in the name of a person
               other than the signer of a Letter of Transmittal, then
               certificates representing the shares of Bargo Common Stock
               surrendered in exchange therefor must be endorsed or accompanied
               by an appropriate instrument of transfer signed exactly as the
               name of the registered owner appears on such certificates, with
               the signatures on the certificates or instruments of transfer
               guaranteed by an Eligible Institution (unless signed by an
               Eligible Institution).

          (f)  If this Letter of Transmittal or any Certificate, proxy or stock
               power is signed by a trustee, executor, administrator, guardian,
               attorney-in-fact, officer of a corporation or other person
               acting in a fiduciary or representative capacity, such person
               must so indicate when signing, and proper evidence satisfactory
               to Mission Resources of their authority to so act must be
               submitted.

          (g)  If this Letter of Transmittal is signed by a person other than
               the registered holder(s) of the shares of Bargo Common Stock
               listed, the Certificate must be endorsed or accompanied by
               appropriate stock powers, in either case signed exactly as the
               name(s) of the registered holder(s) appear(s) on the
               Certificates. Signatures on such Certificates or stock powers
               must be guaranteed by an Eligible Institution (unless signed by
               an Eligible Institution).

         5. Withholding. The Exchange Agent and Mission Resources are entitled
to deduct and withhold from the consideration otherwise payable pursuant to the
Merger described in the Prospectus to any holder of shares of Bargo Common Stock
any amounts that the Exchange Agent or Mission Resources, as the case may be, is
required to deduct and withhold with respect to the making of such payment
under the Internal Revenue Code of 1986 (the "CODE"), or any provision of state,
local or foreign tax law. To the extent that amounts are withheld, the withheld
amounts shall be treated for all purposes as having been paid to the holder of
shares of Bargo Common Stock in respect of which such deduction and withholding
was made.

         6. Special Issuance and Special Delivery Instructions. If the
Mission Common Stock and the Cash Consideration are to be issued and paid to
someone other than the holder or mailed to an address other than that shown
above, the appropriate boxes on this Letter of Transmittal should be completed.

         7. Irregularities. All questions as to the form of documents and the
validity of shares of Bargo Common Stock will be resolved by Mission Resources,
in its sole discretion, whose determination shall be final and binding. Mission
Resources reserves the absolute right to reject any deliveries of any
Certificates for exchange that are not in proper form, or the acceptance of
which would, in the opinion of Mission Resources or its counsel, be unlawful.
Mission Resources reserves the absolute right to waive any defect or
irregularity of delivery for exchange with regard to any shares of Bargo Common
Stock.

         8. Mutilated, Lost, Stolen or Destroyed Certificates. Any holder whose
Certificate(s) have been mutilated, lost, stolen or destroyed should complete
this Letter of Transmittal and attach a letter to it indicating that his/her
Certificate(s) has/have been mutilated, lost, stolen or destroyed and mail or
otherwise deliver both to the Exchange Agent at the address set forth on the
front of this Letter of


<PAGE>   6

Transmittal. The holder will then be instructed as to the steps he/she must take
in order to receive the Certificate(s) representing the Mission Common Stock.

         9. Requests for Assistance or Additional Copies. Requests for
assistance or for additional copies of this Letter of Transmittal may be
directed to the Exchange Agent at one of the addresses or telephone numbers set
forth on the cover of this Letter of Transmittal.

                            IMPORTANT TAX INFORMATION

         Under federal income tax law, a holder who delivers shares of Bargo
Common Stock for exchange is required to provide Mission Resources (as payer),
through the Exchange Agent, with the holder's correct taxpayer identification
number ("TIN") on Substitute Form W-9 or otherwise establish a basis for
exemption from backup withholding. Generally, if the holder is an individual,
the TIN is the holder's social security number. If the Exchange Agent is not
provided with the correct taxpayer identification number, the holder may be
subject to a $50 penalty, as well as various other penalties, imposed by the
Internal Revenue Service. In addition, payments made to the holder with respect
to the Mission Common Stock or the Bargo Common Stock may be subject to backup
withholding.

         Certain holders (including, among others, all corporations and certain
foreign individuals) are not subject to these backup withholding and reporting
requirements. Exempt holders should indicate their exempt status on Substitute
Form W-9. A foreign individual may qualify as an exempt recipient or other
payee by submitting to the Exchange Agent a properly completed Internal Revenue
Service Form W-8 signed under penalty of perjury, attesting to the holder's
exempt status.

         If backup withholding applies, Mission Resources is required to
withhold 31% of any payment made to the holder or other payee. Backup
withholding is not an additional federal income tax. Rather, the amount
withheld will be credited against the federal income tax liability of persons
subject to backup withholding. If withholding results in an overpayment of
taxes, a refund may be obtained from the Internal Revenue Service provided that
the required information is timely furnished to the Internal Revenue Service.

PURPOSE OF SUBSTITUTE FORM W-9

         To prevent backup withholding on payments that are made to a holder
with respect to the Mission Common Stock or the Bargo Common Stock, the holder
is required to provide the Exchange Agent with either: (i) the holder's correct
TIN by completing the form below, certifying that the TIN provided on Substitute
Form W-9 is correct (or that the holder is awaiting a TIN) and that (A) the
holder has not been notified by the Internal Revenue Service that he or she is
subject to backup withholding as a result of failure to report all interest or
dividends or (B) the Internal Revenue Service has notified the holder that he or
she is no longer subject to backup withholding; or (ii) an adequate basis for
exemption.

WHAT NUMBER TO GIVE THE EXCHANGE AGENT

         The holder is required to give the Exchange Agent the TIN (e.g., social
security number or employer identification number) of the record owner of the
Bargo Common Stock.


<PAGE>   7



              TO BE COMPLETED BY ALL HOLDERS OF BARGO COMMON STOCK
        (See Instruction 5 and "Important Tax Information" on this Letter
                                of Transmittal)

<TABLE>
<CAPTION>

                   PAYER'S NAME: MISSION RESOURCES CORPORATION

<S>                                     <C>                             <C>
       SUBSTITUTE                       Part I--PLEASE PROVIDE YOUR         Social Security Number
        FORM W-9                        TIN IN THE BOX AT RIGHT AND
Department of the Treasury              CERTIFY BY SIGNING AND                -----------------
 Internal Revenue Service               DATING BELOW.                              -----
                                                                                     OR
                                                                        Employer Identification Number

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

 Payer's Request for Taxpayer           Name (Please Print)
Identification Number (TIN) and                             -------------------------------
      Certificate                       Address
                                                -------------------------------------------

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

                                        ---------------------------------------------------
                                        City              State                    ZIP Code

                                        Part 2--Awaiting TIN  [ ]


Part 3--CERTIFICATION--UNDER THE PENALTIES OF PERJURY, I CERTIFY THAT (1) the
number shown on this form is my correct taxpayer identification number (or a TIN
has not been issued to me but I have mailed or delivered an application to
receive a TIN or intend to do so in the near future), (2) I am not subject to
backup withholding either because I have not been notified by the Internal
Revenue Service (the "IRS") that I am subject to backup withholding as a result
of a failure to report all interest or dividends or the IRS has notified me that
I am no longer subject to backup withholding, and (3) all other information
provided on this form is true, correct and complete.


Signature                                    Date
          --------------------------------        ------------------------------


You must cross out item (2) above if you have been notified by the IRS that you
are currently subject to backup withholding because of under-reported interest
or dividends on your tax return and you have not been advised by the IRS that
such backup withholding has been terminated.
</TABLE>

   FAILURE TO COMPLETE AND RETURN THIS FORM MAY RESULT IN BACKUP WITHHOLDING.


               YOU MUST COMPLETE THE FOLLOWING CERTIFICATE IF YOU
                CHECKED THE BOX IN PART 2 OF SUBSTITUTE FORM W-9



<PAGE>   8

             CERTIFICATE OF AWAITING TAXPAYER IDENTIFICATION NUMBER

I certify under the penalties of perjury that a taxpayer identification number
has not been issued to me, and either (a) I have mailed or delivered an
application to receive a taxpayer identification number to the appropriate
Internal Revenue Service Center or Social Security Administration Office or (b)
I intend to mail or deliver an application in the near future. I understand that
if I do not provide a taxpayer identification number within sixty (60) days,
31% of all reportable payments made to me thereafter will be withheld until I
provide a number.


Signature                                            Date
         ------------------------------------------      -----------------------