PVT PLT IN A BE58 ENTERS RWY 28R DURING A DEP BY AN ACR B737. RPTR ALLEGES THAT THERE WAS NO TXWY SIGN FOR IDENTING TXWY C WHEN LEAVING THE FBO AT SFO. B737 AIRBORNE ABOUT 1200 FT PRIOR TO TXWY E; THE BE58'S ESCAPE RTE.

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PRE-FILED IFR FROM SFO TO MODESTO. CLRED TO TAXI RWY 28R VIA TXWY C. RAINING; FAIR TO POOR VISIBILITY. NO SIGN DESIGNATING TXWY C WHEN EXITING FBO. TAXIING SLOWLY AND DOUBLE-CHKING SHORELINE 9 DEP. RWYS 28R AND 28L ACTIVE RWYS THIS AM. TAXIED ONTO RWY 28R AT TXWY K. WHEN ON RWY 28R (ACTIVE RWY) SAW PAX JET ON THRESHOLD OTHER END FACING ME. REALIZED I WAS ON RWY 28R AND NOT TXWY C. HEADED STRAIGHT AWAY TO TXWY E (NEXT EXIT E OF TXWY K) AND SIMULTANEOUSLY HEARD GND CTL SAY: 'TURN L AT TXWY.' (THIS WAS TXWY E.) WHEN ON TXWY E AND OFF RWY 28R; PAX JET THAT WAS APPARENTLY CLRED FOR TKOF RWY 28R WAS ALREADY OFF THE GND AT LEAST 2000 FT AHEAD OF ME. BY THE TIME PAX JET WAS AT TXWY E; I ESTIMATE AT 400-600 FT ABOVE GND. FACTORS AFFECTING QUALITY OF PERFORMANCE: FIRST TIME IN 5 YRS THIS PLT GIVEN SHORELINE 9 DEP. SOME DEG OF INATTENTION TO TAXIING WHILE DOUBLE-CHKING SHORELINE DEP. CONTRIBUTING FACTORS: 1) FAIR-POOR GND VISIBILITY: RAINING; 2) NO SIGN DESIGNATING TXWY C; 3) SMALL ON-THE-GND DESIGNATING SIGN FOR RWY 28R; AND 4) ? NO WARNING FROM TWR THAT I HAD CROSSED TXWY C AND WAS HEADING TO RWY 28R. I THINK IT WAS A COMBINATION OF FACTORS THAT CAUSED THIS INCIDENT: PARTLY THIS PLT'S INATTENTION; RAIN AND POOR VISIBILITY; NO SIGN FOR TXWY C.