<PAGE>
 
                                 EXHIBIT 24.1


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

          I hereby appoint CRAIG E. GASS, CHERYL SOROKIN, and R. SCOTT MCMILLEN,
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 1997, and any amendments.


Dated:  March 13, 1998
        --------------

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

          I hereby appoint CRAIG E. GASS, CHERYL SOROKIN, and R. SCOTT MCMILLEN,
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 10-K annual report for 1997, and any amendments.


Dated:  March 13, 1998
        --------------
                                    /s/  Sharif M. Bayyari    
                                    ---------------------------
                                    Sharif M. Bayyari
                                    President and Chief Executive Officer
<PAGE>
 
                               POWER OF ATTORNEY
                               -----------------

          I hereby appoint CRAIG E. GASS, CHERYL SOROKIN, and R. SCOTT MCMILLEN,
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
1997, and any amendments.


Dated:  March 13, 1998
        --------------
                                    /s/ Barbara Desoer
                                    ------------------
                                    Barbara Desoer
                                    Director
<PAGE>
 
                               POWER OF ATTORNEY
                               -----------------

          I hereby appoint CRAIG E. GASS, CHERYL SOROKIN, and R. SCOTT MCMILLEN,
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
1997, and any amendments.


Dated:  March 13, 1998
        --------------
                                    /s/ H. Eugene Lockhart
                                    ----------------------
                                    H. Eugene Lockhart
                                    Director
<PAGE>
 
                               POWER OF ATTORNEY
                               -----------------

          I hereby appoint CRAIG E. GASS, CHERYL SOROKIN, and R. SCOTT MCMILLEN,
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
1997, and any amendments.


Dated:  March 13, 1998
        --------------
                                    /s/ William E. Fisher
                                    ---------------------
                                    William E. Fisher
                                    Director
<PAGE>
 
                               POWER OF ATTORNEY
                               -----------------

          I hereby appoint CRAIG E. GASS, CHERYL SOROKIN, and R. SCOTT MCMILLEN,
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
1997, and any amendments.


Dated:  March 13, 1998
        --------------
                                    /s/ Donald R. Dixon
                                    -------------------
                                    Donald R. Dixon
                                    Director
<PAGE>
 
                               POWER OF ATTORNEY
                               -----------------

          I hereby appoint CRAIG E. GASS, CHERYL SOROKIN, and R. SCOTT MCMILLEN,
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
1997, and any amendments.


Dated:  March 13, 1998
        --------------
                                    /s/ James H. Williams
                                    ---------------------
                                    James H. Williams
                                    Executive Vice President