<PAGE>   1

                UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 10-K

[X]     ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
        ACT OF 1934

FOR THE FISCAL YEAR ENDED:  DECEMBER 31, 1999

                                       OR

[ ]     TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES ACT
        OF 1934

FOR THE TRANSITION PERIOD FROM __________ TO _________.

COMMISSION FILE NUMBER:  333-9532

BEAR STEARNS ASSET BACKED SECURITIES, INC. (AS DEPOSITOR UNDER THE DEPOSIT TRUST
AGREEMENT, DATED APRIL 1, 1999, PROVIDING FOR THE ISSUANCE OF THE AMERICAN
RESIDENTIAL EAGLE BOND TRUST MORTGAGE BACKED LIBOR NOTES, CLASS A, SERIES
1999-1)

                   BEAR STEARNS ASSET BACKED SECURITIES, INC.
             (Exact Name of registrant as specified in its charter)

<TABLE>
<S>                                                 <C>
                    DELAWARE                                     13-3836437
(State or other jurisdiction of incorporation or    (I.R.S. employer identification no.)
                  organization)

                 245 PARK AVENUE                                    10167
                  NEW YORK, NY                                   (Zip code)
    (Address of principal executive offices)
</TABLE>

                                 (212) 272-4095
              (Registrant's telephone number, including area code)

<TABLE>
<S>                                                              <C>
Securities registered pursuant to Section 12(b) of the Act:      Securities registered pursuant to Section 12(g) of the Act:

                          NONE                                                                 NONE
                    (Title of class)                                                      (Title of class)
</TABLE>

Indicate by check mark whether the Registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the Registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days. Yes [X] No [ ]

Indicate by check mark if disclosure of delinquent filers pursuant to Item 405
of Regulation S-K is not contained herein, and will not be contained, to the
best of Registrant's knowledge, in definitive proxy or information statements
incorporated by reference in Part III of this Form 10-K or any amendment to this
Form 10-K. [X]

State the aggregate market value of the voting stock held by non-affiliates of
Registrant. The aggregate market value shall be computed by reference to the
price at which the stock was sold, or the average bid and asked prices of such
stock, as of specified date within 60 days prior to the date of filing:

                                  NOT APPLICABLE

                       Documents incorporated by reference:

                                  NOT APPLICABLE



<PAGE>   2

                   BEAR STEARNS ASSET-BACKED SECURITIES, INC.
                   MORTGAGE-BACKED LIBOR NOTES, SERIES 1999-1

                                      INDEX

<TABLE>
<CAPTION>
                                                                                                  Page
                                                                                                  ----
<S>       <C>                                                                                     <C>
PART I    ....................................................................................     3
          ITEM 1  -  BUSINESS.................................................................     3
          ITEM 2  -  PROPERTIES...............................................................     3
          ITEM 3  -  LEGAL PROCEEDINGS........................................................     3
          ITEM 4  -  SUBMISSION OF MATTERS TO A VOTE OF
                     SECURITY HOLDERS.........................................................     3

PART II   ....................................................................................     3
          ITEM 5  -  MARKET FOR REGISTRANT'S COMMON STOCK AND
                     RELATED STOCKHOLDER MATTERS..............................................     3
          ITEM 6  -  SELECTED FINANCIAL DATA..................................................     3
          ITEM 7  -  MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                     FINANCIAL CONDITION AND RESULTS OF OPERATIONS............................     3
          ITEM 8  -  FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA..............................     3
          ITEM 9  -  CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS
                     ON ACCOUNTING AND FINANCIAL DISCLOSURE...................................     3

PART III  ....................................................................................     4
          ITEM 10 -  DIRECTORS AND EXECUTIVE OFFICERS OF
                     THE REGISTRANT...........................................................     4
          ITEM 11 -  EXECUTIVE COMPENSATION...................................................     4
          ITEM 12 -  SECURITY OWNERSHIP OF CERTAIN BENEFICIAL
                     OWNERS AND MANAGEMENT....................................................     4
          ITEM 13 -  CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS...........................     4

PART IV   ....................................................................................     5
          ITEM 14 -  EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND
                     REPORTS ON FORM 8-K......................................................     5

SIGNATURES     ...............................................................................     6
INDEX TO EXHIBITS.............................................................................     7
</TABLE>
<PAGE>   3

                                      PART I

ITEM 1 -    BUSINESS

            Not Applicable.

ITEM 2   -  PROPERTIES

            Bear Stearns Asset-Backed Securities, Inc. (the "Depositor") will
furnish information regarding the Mortgaged Properties by reference to the
Annual Compliance Certificates to be filed herein under Item 14.

ITEM 3   -  LEGAL PROCEEDINGS

            The Depositor is not aware of any material pending legal proceedings
involving either the Mortgage-Backed LIBOR Notes, Series 1999-1, the American
Residential Eagle Bond Trust 1999-1 (the "Trust); the Master Servicing
Agreement; the Deposit Trust agreement; the Master Servicer; the Trustee; the
Depositor; or the Servicer which relates to the Trust.

ITEM 4   -  SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

            No matter has been submitted to a vote of the holders of beneficial
interests in the Trust through the solicitation of proxies or otherwise.

                                      PART II

ITEM 5   -  MARKET FOR REGISTRANT'S COMMON STOCK AND RELATED STOCKHOLDER MATTERS

            To the best knowledge of the Depositor, there is no established
public trading market for the Notes.

            The Class A Note issued by the Trust is held by the Depository Trust
Company ("DTC") which in turn maintains records of holders of beneficial
interests in the Note. Based on information obtained by the Trust from DTC, as
of December 31, 1999, there were ten holders of Class A Note.

ITEM 6   -  SELECTED FINANCIAL DATA

            Not Applicable.

ITEM 7   -  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
            RESULTS OF OPERATIONS

            Not Applicable.

ITEM 8   -  FINANCIAL STATEMENTS AND SUPPLEMENTARY INFORMATION

            Not Applicable.

ITEM 9   -  CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING AND
            FINANCIAL DISCLOSURE

            There were no changes of accountants or disagreements on accounting
or financial disclosures between the Depositor and its accountants.



<PAGE>   4

                                     PART III

ITEM 10  -  DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT

            Not Applicable.

ITEM 11  -  EXECUTIVE COMPENSATION

            Not Applicable.

ITEM 12  -  SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT

            The Depositor is a wholly-owned, special purpose subsidiary of The
Bear Stearns Companies Inc., a Delaware corporation. The Trust is a Delaware
statutory business trust wholly-owned by the Depositor.

ITEM 13  -  CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS

            None.



<PAGE>   5

                                      PART IV

ITEM 14  -  EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM 8-K

            (a) The following documents are filed as part of this report:

                1.  Financial Statements:

                    Not applicable.

                2.  Financial Statement Schedules:

                    Not applicable.

                3.  Exhibits:

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<CAPTION>
                    Exhibit No.           Description
                    -----------           -----------
<S>                                       <C>
                    99.1*                 Statement of Compliance of the
                                          Master Servicer pursuant to Section
                                          3(s) of the Master Servicing Agreement.

                    99.2*                 Annual Report of Independent
                                          Accountant with respect to the
                                          Master Servicer's overall
                                          servicing operations pursuant to
                                          Section 3(t) of the Master Servicing
                                          Agreement.
</TABLE>

--------------
*The document is not due to be delivered until April 30, 2000. Such document
will be filed with the Securities and Exchange Commission by amendment upon
receipt by the Registrant.


<PAGE>   6

                                   SIGNATURES


            Pursuant to the requirements of Section 13 or 15(d) of the
Securities Exchange Act of 1934, the Depositor has duly caused this Report to be
signed on its behalf by the undersigned, thereunto duly authorized.


                                            By: BEAR STEARNS ASSET BACKED
                                                SECURITIES, INC.,
                                                As Depositor


                                               By: /s/ JOSEPH T. JURKOWSKI, JR.
                                                  ------------------------------
                                               Name: Joseph T. Jurkowski, Jr.
                                               Title: Vice President, Secretary

Date: March 30, 2000.

         Pursuant to the requirements of the Securities Exchange Act of 1934,
this Report has been signed below by the following persons on behalf of the
Depositor and in the capacities and on the dates indicated:


<TABLE>
<CAPTION>
      Signature                      Position                         Date
      ---------                      --------                         ----
<S>                                  <C>                           <C>

/s/ PATRICIA A. JEHLE                Chief Executive Officer,      March 30, 2000
---------------------------          President, Director
    Patricia A. Jehle


/s/ JULIANA C. JOHNSON               Director                      March 30, 2000
---------------------------
    Juliana C. Johnson


/s/ THOMAS MARANO                    Director                      March 30, 2000
---------------------------
    Thomas Marano


/s/ JEFFREY MAYER                    Director                      March 30, 2000
---------------------------
    Jeffrey Mayer


/s/ SAMUEL L. MOLINARO, JR.          Treasurer                     March 30, 2000
---------------------------
    Samuel L. Molinaro, Jr.

</TABLE>



<PAGE>   7

                                INDEX TO EXHIBITS
                                   Item 14(C)

<TABLE>
<CAPTION>
Exhibit No.   Description
-----------   -----------
<S>           <C>
99.1*         Statement of Compliance of the Master Servicer pursuant to Section
              3(s) of the Master Servicing Agreement.

99.2*         Annual Report of Independent Accountant with respect to the Master
              Servicer's overall servicing operations pursuant to Section 3(t) of
              the Master Servicing Agreement.
</TABLE>

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*The document is not due to be delivered until April 30, 2000. Such document
will be filed with the Securities and Exchange Commission by amendment upon
receipt by the Registrant.