NMAC. VFR ACFT SEE AND AVOID.

Narrative

I WAS ON A VFR FLT FROM AUBURN; CA (AUN) TO SAN JOSE; CA (SJC); RECEIVING FLT FOLLOWING SERVICES ALONG THE RTE. AS STOCKTON APCH HANDED ME OFF TO BAY APCH ON 135.4; I WAS SLOWLY DSNDING THROUGH 6000 FT. I INCREASED MY RATE OF DSCNT WHEN BAY REQUESTED TO MAINTAIN AT OR BELOW 5000 FT FOR TFC. ABOUT 5 NM ESE OF THE LIVERMORE; CA (LVK) ARPT; BAY ISSUED A TA 10 O'CLOCK AND REQUESTED IMMEDIATE DSCNT TO 3000 FT. I DSNDED TO 3000 FT AT A RATE GREATER THAN 1500 FPM. BOTH MY PAX AND I; AN ATP-MEL AND COMMERCIAL HELI PLT SCANNED NOT ONLY OUR 10 O'CLOCK BUT THE FULL AREA. ARRIVING AT 3000 FT; WE FOUND IT -- AT OUR 2 O'CLOCK POS: A MOONEY (POSSIBLY A CHEROKEE); WHITE/BLUE; WAS HEADED STRAIGHT AT US. BOTH ACFT TOOK EVASIVE ACTION TO THE L. WE WERE BASICALLY AT THE SAME ALT AND MISSED BY APPROX 200 FT LATERALLY. MY IMMEDIATE CALL TO THE CTLR WAS IGNORED. HIS NEXT COM FOR ME WAS SEVERAL MINS LATER; AS I WAS APCHING THE SUNOL INTXN; WHEN HE INSTRUCTED ME TO CONTACT STOCKTON APCH ON 123.85. SINCE STOCKTON IS TO THE NE OF THIS SECTOR OF BAY APCH AND I WAS LEAVING THE SECTOR TO THE SW; I TOLD HIM THAT I WOULD BE CONTACTING BAY APCH ON 121.3. HE COPIED THAT.