A CPR FLC FLYING AN HS125-800 AT SJC RPTS MISUNDERSTANDING WITH GND CTL AFTER COMPLYING WITH TAXI INSTRUCTIONS.

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OUR ACFT WAS PARKED AT SAN JOSE FBO #1. PNF CALLED GND CTL TO REPOSITION FROM FBO #1 TO FBO #2 ON THE OTHER SIDE OF THE FIELD. WE WERE TOLD TAXI VIA TXWY V TO TXWY C; HOLD SHORT RWY 30L ON TXWY C. AN ACR B737 LANDED. WE WERE THEN CLRED TO CROSS RWYS 30L AND 30R TAXI TO FBO #2. WE DID ALL THIS AND EVERYTHING WAS FINE. WE HAD A PAX TO DROP OFF; THEN PNF CALLED GND CTL THAT WE WERE READY TO TAXI OUT OF FBO #2 WITH OUR IFR CLRNC AND ATIS INFO. (HERE IS WHERE THE PROB STARTS.) BOTH PLTS UNFAMILIAR WITH SAN JOSE. GND CTL INSTRUCTIONS WERE TO 'TAXI TO RWY 30L.' THERE WAS NO MENTION OF ANY TURNS; PROCEED WITH CAUTION; OR HOLD SHORT OF ANY TXWYS OR RWYS. A CLRNC TO TAXI TO AN ACTIVE RWY WITH NOTHING ELSE SAID IS A CLRNC TO CROSS TXWY OR RWY TO GET TO THAT RWY. THE MOST DIRECT RTE TO RWY 30L WAS THE WAY WE HAD JUST BEEN CLRED TO COME ACROSS. WE CAME STRAIGHT OUT OF FBO #2 ONTO TXWY C; CROSSED THE APCH END OF RWY 30R ON TXWY C AND HELD SHORT OF RWY 30L. PNF CALLED TWR THAT WE WERE READY FOR TKOF; THEY THEN CLRED US INTO POS AND TAKE THIS PHONE NUMBER BECAUSE WE HAD A RWY AND TXWY PLTDEV. THERE WERE NO ACFT ON FINAL OF RWYS 30R; 30L OR ON ANY TXWYS AROUND US. THERE MAY HAVE BEEN LACK OF COM OR MISUNDERSTANDING ON BOTH OUR PART AND GND CTL; BUT DEFINITELY NOTHING INTENTIONAL ON OUR PART. WE DID CALL THE TWR TWICE AND TALKED TO THE SUPVR; WHO THEN TOLD US THAT HE DID NOT FEEL THERE WOULD BE ANY VIOLATIONS; BUT A RPT WAS TO BE FILED. SUPPLEMENTAL INFO FROM ACN 452103: WE WERE PARKED ON THE RAMP AT THE SAN JOSE FBO #1. WE CALLED GND FOR TAXI INSTRUCTIONS TO REPOSITION TO THE FBO #2 RAMP ON THE OPPOSITE SIDE OF THE AIRFIELD TO DROP OFF A PAX. WE WERE CLRED TO TAXI VIA TXWYS V AND C WITH INSTRUCTIONS TO HOLD SHORT OF RWY 30L AT TXWY C. AFTER AN AIRPLANE LANDED ON RWY 30L WE WERE CLRED TO TAXI TO THE FBO #2 RAMP BY XING RWYS 30L AND 30R. WE DROPPED OFF OUR PAX AT FBO #2 AND THEN REQUESTED TAXI CLRNC TO THE ACTIVE RWY 30L. GND CLRED US TO TAXI TO RWY 30L WITHOUT ANY OTHER TAXI INSTRUCTIONS. WE FEEL; AND SO DID THE TWR SUPVR; THAT THIS IS WHERE THE MISUNDERSTANDING/DEV OCCURRED BTWN US AND GND CTL. WHEN WE WERE CLRED TO TAXI TO RWY 30L WE ASSUMED WE WERE CLRED TO TAXI BACK OUT TO RWY 30L THE SAME WAY WE CAME IN. THIS TAXI RTE TOOK US ACROSS THE APCH END OF RWY 30R WHICH WE THOUGHT WE WERE CLRED TO CROSS WITH OUR CLRNC TO TAXI TO RWY 30L. GND CTL EXPECTED US TO TAXI A DIFFERENT WAY TO THE DISPLACED THRESHOLD FOR RWY 30L. WHEN WE APCHED THE HOLD SHORT OF RWY 30L WE RECEIVED CLRNC TO TAKE OFF AND WERE GIVEN A PHONE NUMBER TO CALL THE TWR SUPVR. WE CALLED THE TWR SUPVR AND HE INFORMED US OF THE POSSIBLE PLTDEV. HE HAD REVIEWED THE TAPES AND STATED THAT HE COULD SEE WHERE THE MISUNDERSTANDING OCCURRED BTWN OUR ACFT AND GND CTL.