A PLT EXPERIENCED POSITIONAL AWARENESS LOSS WHILE ATTEMPTING TO TRAVERSE BAY APCH AIRSPACE IN MVFR CONDITIONS. AFTER INADVERTENTLY ENTERING CLASS C; THE PLT HAD AN NMAC WITH A BUSINESS JET.

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I WAS RETURNING TO THE BAY AREA FROM COLUMBIA; CA. MY DEST WAS SAN CARLOS ARPT. I WAS 2 MI W OF LIVERMORE ARPT; WHEN I TUNED IN HWD ATIS; AND DISCOVERED THAT HWD'S ATA HAD 4 MI VISIBILITY AND A CEILING OF 800 FT. I DECIDED TO FLY AROUND THE STRATUS BY FLYING S OVER THE CITY OF FREMONT. I INADVERTENTLY FLEW INTO THE SAN JOSE CLASS C AND I MISSED COLLIDING WITH A BUSINESS JET BY ABOUT 1/2 MI; BY ROLLING INTO A CLBING L TURN. I CONTACTED BAY APCH AND REQUESTED A CLRNC THROUGH THE CLASS C AIRSPACE ENRTE TO SAN CARLOS. APCH ADVISED ME THAT HE HAD TO VECTOR TFC AROUND ME FOR COLLISION AVOIDANCE. HE ALSO ADVISED ME THAT I WAS 2 MI E OF MOFFETT WHEN THE NEAR MIDAIR OCCURRED. I WAS THEN GIVEN A XPONDER CODE TO SQUAWK AND CLRNC THROUGH THE CLASS C AIRSPACE. NO FURTHER PROBS WERE ENCOUNTERED FLYING BACK TO SQL. I SHOULD HAVE CONTACTED BAY APCH EARLIER; AND REQUESTED A CLRNC THROUGH THE SAN FRANCISCO CLASS B AIRSPACE; SO THAT I COULD HAVE FLOWN ON TOP OF THE BROKEN STRATUS CLOUDS; AND I SHOULD HAVE KEPT BETTER TRACK OF MY POS WITH REGARD TO SJC CLASS C AIRSPACE; TOO.