A PA28 PVT PLT HAS A POTENTIAL CONFLICT AT 8500 FT WITH A B737 E MI SE OF HWD ARPT; CA.

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I EXPERIENCED AN NMAC IN CLASS B AIRSPACE BECAUSE I BELIEVE ATC DID NOT UNDERSTAND MY RPT THAT I HAD LOST VISUAL CONTACT WITH RPTED TFC. FLYING VFR FROM SBA TO STS; I HAD RECEIVED CLRNC THROUGH THE SAN FRANCISCO CLASS B AIRSPACE FROM BAY APCH. I RECEIVED THE CLRNC WHEN I WAS ABOUT 4 MI E OF SJC (OUTSIDE THE CLASS B AIRSPACE) AND WAS CLRED DIRECT SGD VOR AT 8500 FT. THE GND TRACK FROM THAT POS TO SGD WAS APPROX 320 DEGS. IN THE VICINITY OF 3 MI SE HWD ARPT; TO THE BEST OF MY RECOLLECTION; THE FOLLOWING COMS TOOK PLACE -- BAY APCH: RPTR; TFC 3 O'CLOCK; B737; 11000 FT; SWBOUND; DSNDING. RPTR: TFC IN SIGHT. BAY APCH: RPTR; TURN HDG 270 DEGS FOR TFC. RPTR: THAT'S A L TURN 270 DEGS. (I BEGAN THE TURN.) ABOUT 20 SECONDS LATER; RPTR; APCH; I HAVE LOST SIGHT OF THAT B737 BEHIND MY WIND. ABOUT 20 SECONDS LATER; RPTR: APCH; I HAVE LOST SIGHT OF THAT B737 AT MY 6 O'CLOCK POS. ABOUT 15 SECONDS LATER; BAY APCH: (SAID SOMETHING BUT I FORGOT WHAT. I DO NOT BELIEVE IT WAS AN ACKNOWLEDGEMENT OF THE LOST VISUAL CONTACT; A VECTOR OR POS RPT OF THE TFC.) ABOUT 30 SECONDS LATER; BAY APCH: RPTR; RESUME OWN NAV. RPTR: OWN NAV. (AT THIS POINT I ASSUMED THE TFC WAS NO FACTOR.) AFTER TURNING BACK TO HG 320 DEGS; THE B737 PASSED IN FRONT OF ME; WITH ABOUT 900 FT LATERAL AND 200 FT VERT SEPARATION. THEN; TO THE BEST OF MY RECOLLECTION; THE FOLLOWING COMS TOOK PLACE -- RPTR: APCH; THAT B737 PASSED PRETTY CLOSE TO ME. BAY APCH: WEREN'T YOU IN VISUAL CONTACT WITH HIM? RPTR: NEGATIVE SIR; I RPTED EARLIER THAT I LOST CONTACT WITH HIM. THAT WAS THE LAST RELEVANT COM WITH THIS CTLR; AND I PROCEEDED TO SGD-STS AND LANDED WITHOUT INCIDENT.