A319 CREW AND A GA ACFT HAD AN NMAC OVER THE SAN MATEO BRIDGE IN SFO CLASS B.

Narrative

APCHING THE SAN MATEO BRIDGE ON THE SFO FMS RWY 28R APCH; WE WERE DSNDING IN CLR WX TOWARD 1800 FT MSL. TCASII DISPLAYED A PROXIMATE TARGET AT OUR 1 O'CLOCK POS; AT A DISTANCE APPROX AT THE LOCATION OF THE BRIDGE. WE SCANNED AND VISUALLY ACQUIRED A GA ACFT FLYING FROM OUR R TO L AT THE SAME TIME THAT OUR TCASII GENERATED AN RA 'MONITOR VERT SPD.' WE STOPPED OUR DSCNT AT 2300 FT MSL IN COMPLIANCE WITH THE RA AND WATCHED THE GA ACFT PASS DIRECTLY BENEATH US. WE WERE PRECISELY ON THE SFO 095 DEG RADIAL JUST OUTSIDE THE BRIDGE. TCASII SHOWED THE ACFT TO BE 400 FT BELOW OUR ALT. WE RPTED THESE EVENTS TO NORCAL APCH CTL AS THEY OCCURRED. THEY HAD NEVER POINTED OUT THE ACFT TO US. THE CTLR RESPONDED THAT THEY WOULD TAKE CARE OF IT. HAD WE NOT HAD TCASII; AND HAD WE THEN CONTINUED ON A NORMAL DSCNT TOWARD THE PUBLISHED XING ALT OF 1800 FT MSL AT THE BRIDGE AND NOT VISUALLY ACQUIRED AND SUBSEQUENTLY MANEUVERED TO AVOID THAT ACFT; WE WOULD HAVE COLLIDED. NO ABRUPT MANEUVERING WAS EVER REQUIRED DURING THIS EVENT; AND WE CONTINUED TO A NORMAL STABILIZED APCH AND LNDG.