<PAGE>
 
                                  EXHIBIT 24.1


                               POWER OF ATTORNEY
                               -----------------

          I hereby appoint CRAIG E. GASS, MARLENE A. SHARLAND, and EDWARD J.
STARK, and each of them, my attorneys-in-fact, each with full power of
substitution, to sign for me as Director and Chairman of the Board of BA
Merchant Services, Inc. and file with the Securities and Exchange Commission the
Corporation's Form 10-K annual report for 1998, and any amendments.


Dated:  March 30, 1999

                                            /s/ James G. Jones
                                            ------------------
                                            James G. Jones
                                            Chairman of the Board
<PAGE>
 
                               POWER OF ATTORNEY
                               -----------------

          I hereby appoint CRAIG E. GASS, MARLENE A. SHARLAND, and EDWARD J.
STARK, and each of them, my attorneys-in-fact, each with full power of
substitution, to sign for me as Director and President and Chief Executive
Officer of BA Merchant Services, Inc. and file with the Securities and Exchange
Commission the Corporation's Form 10K annual report for 1998, and any
amendments.


Dated:  March 30, 1999
                                            /s/  Sharif M. Bayyari 
                                            -----------------------------
                                            Sharif M. Bayyari
                                            President and Chief Executive 
                                            Officer
<PAGE>
 
                               POWER OF ATTORNEY
                               -----------------

          I hereby appoint CRAIG E. GASS, MARLENE A. SHARLAND, and EDWARD J.
STARK, and each of them, my attorneys-in-fact, each with full power of
substitution, to sign for me as a Director of BA Merchant Services, Inc. and
file with the Securities and Exchange Commission the Corporation's Form 10-K
annual report for 1998, and any amendments.


Dated:  March 30, 1999
                                            /s/ Barbara J. Desoer
                                            ---------------------
                                            Barbara J. Desoer
                                            Director
<PAGE>
 
                               POWER OF ATTORNEY
                               -----------------

          I hereby appoint CRAIG E. GASS, MARLENE A. SHARLAND, and EDWARD J.
STARK, and each of them, my attorneys-in-fact, each with full power of
substitution, to sign for me as a Director of BA Merchant Services, Inc. and
file with the Securities and Exchange Commission the Corporation's Form 10-K
annual report for 1998, and any amendments.


Dated:  March 30, 1999
                                            /s/ Christopher A. Callero
                                            --------------------------
                                            Christoper A. Callero
                                            Director
<PAGE>
 
                               POWER OF ATTORNEY
                               -----------------

          I hereby appoint CRAIG E. GASS, MARLENE A. SHARLAND, and EDWARD J.
STARK, and each of them, my attorneys-in-fact, each with full power of
substitution, to sign for me as a Director of BA Merchant Services, Inc. and
file with the Securities and Exchange Commission the Corporation's Form 10-K
annual report for 1998, and any amendments.


Dated:  March 30, 1999
                                            /s/ William E. Fisher
                                            ---------------------
                                            William E. Fisher
                                            Director
<PAGE>
 
                               POWER OF ATTORNEY
                               -----------------

          I hereby appoint CRAIG E. GASS, MARLENE A. SHARLAND, and EDWARD J.
STARK, and each of them, my attorneys-in-fact, each with full power of
substitution, to sign for me as a Director of BA Merchant Services, Inc. and
file with the Securities and Exchange Commission the Corporation's Form 10-K
annual report for 1998, and any amendments.


Dated:  March 30, 1999
                                            /s/ Donald R. Dixon
                                            -------------------
                                            Donald R. Dixon
                                            Director
<PAGE>
 
                               POWER OF ATTORNEY
                               -----------------

          I hereby appoint CRAIG E. GASS, MARLENE A. SHARLAND, and EDWARD J.
STARK, and each of them, my attorneys-in-fact, each with full power of
substitution, to sign for me as Executive Vice President, Chief Financial
Officer, Chief Accounting Officer and Treasurer of BA Merchant Services, Inc.
and file with the Securities and Exchange Commission the Corporation's Form 10-K
annual report for 1998, and any amendments.


Dated:  March 30, 1999
                                            /s/ James H. Williams
                                            ---------------------
                                            James H. Williams
                                            Executive Vice President
<PAGE>
 
                               POWER OF ATTORNEY
                               -----------------

          I hereby appoint CRAIG E. GASS, MARLENE A. SHARLAND, and EDWARD J.
STARK, and each of them, my attorneys-in-fact, each with full power of
substitution, to sign for me as a Director of BA Merchant Services, Inc. and
file with the Securities and Exchange Commission the Corporation's Form 10-K
annual report for 1998, and any amendments.


Dated:  March 30, 1999
                                            /s/ Hatim A. Tyabji
                                            -------------------
                                            Hatim A. Tyabji
                                            Director