SMA X HAD CONFLICT WITH ACR IN OAK ARSA. EVASIVE ACTION TAKEN.

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I WAS ON A VFR FLT FROM O88 TO SQL. I AM VERY FAMILIAR WITH THIS RTE; WHICH IS; AFTER TKOF; TO TURN TO A MAGNETIC HDG OF APPROX 198 DEGS; CALL TRAVIS APCH AT 2000 FT FOR FLT FOLLOWING AND COORDINATE WITH BAY APCH FOR AN ARSA CLRNC THROUGH OAKLAND'S AIRSPACE; CLB TO 4500 FT; TRACK INBOUND TO OAK VOR; EXPECT 2000 FT XING THE VOR; BE SWITCHED TO OAK N TWR; THEN BE SWITCHED AGAIN TO OAK S TWR; DSND TO 1400 FT AFTER XING THE SHORELINE; 'CROSS THE MID-SPAN OF THE SAN MATEO BRIDGE; SQUAWK 1200; CONTACT SAN CARLOS TWR.' I WAS TOLD TO CONTACT OAK N TWR ON 118.30. I CALLED N TWR; CONFIRMED THAT I WOULD CROSS THE RWY 29 APCH LIGHTS AT 2000 FT; LEVELED OFF AT 2000 FT ABOUT A MI BEFORE THE APCH LIGHTS. SO FAR EVERYTHING WAS NORMAL. JUST ABOUT THE TIME THAT I WAS WITHIN A QUARTER MI OR SO FROM THE MIDDLE OF THE RWY 29 APCH LIGHTS SEVERAL THINGS HAPPENED. FIRST; I WONDERED WHY I HADN'T YET BEEN SWITCHED TO THE S TWR. I LOOKED TO THE S AND SAW A JET APCHING OAK. IT APPEARED TO BE WITHIN 2 MI AND SLIGHTLY ABOVE MY ALT. IT APPEARED TO ENTER A STEEP TURN; AND I HAVE NEVER SEEN AN AIRLINER DO THAT BEFORE. I THEREFORE ADDED THROTTLE TO SPD UP; TURNED PERPENDICULAR TO THE RWY (FLEW W A BIT); AND DOVE STEEPLY OUT OF ANY CONCEIVABLE PATH OF THIS JET. DURING THIS TIME; OAK N TWR FINALLY HANDED ME OFF TO THE S TWR; BUT I WAS UNABLE TO RAISE THEM; AND SO I TRIED BAY APCH. I THEN SWITCHED BACK TO OAK S TWR AND THIS TIME I WAS ABLE TO MAKE CONTACT. I TOLD THEM THAT I HAD BEEN UNSUCCESSFUL IN RAISING THEM BEFORE. OAK S TWR ADVISED ME OF THE SMA THAT WAS IN FRONT OF ME AT 1300 FT AND I ACKNOWLEDGED HAVING IT IN SIGHT. THERE WAS NO MENTION OF THE JET AT ALL. OAK S TWR THEN HAD BOTH OF US (INDIVIDUALLY) SQUAWK AND TOLD US EACH TO CONTACT SAN CARLOS.