GULFSTREAM GIV FLT CREW HAS A RWY INCURSION AT OAK.

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WE WERE DISPATCHED TO OAK TO REPLACE AN OWNER'S ACFT THAT WAS UNAIRWORTHY DUE TO MECHANICAL DISCREPANCY. THE RELIEF CREW WAS BRIEFED BY THE OWNER'S CHIEF PLT THAT THE PAX WAS VERY ECCENTRIC AND FEARFUL OF FLYING. HE REQUESTED WE DO OUR BEST TO ACCOMMODATE THE ECCENTRICITIES OF THE PAX TO THE ACFT; WHICH CREATED A SHORT DELAY TO GET AVIONICS; INS; ETC; ONLINE ONCE APU WAS STARTED. NO SHARP TURNS DURING TAXI; THE PAX DIDN'T WANT TO FEEL THE ACCELERATION DURING THE TKOF ROLL; NO HIGH DECK ANGLES; AND LIMIT ACFT ALT TO 27000 FT TO KEEP THE CABIN ALT AT SEA LEVEL. SEVERAL REQUESTS THAT REQUIRED DEVIATION FROM NORMAL COCKPIT PROC. THE FO REQUESTED RWY 29 FOR DEP TO GIVE US 10000 FT OF RWY AND MINIMIZE THE ACCELERATION WHILE APPLYING POWER ON THE TKOF ROLL. UPON REACHING THE INTXN OF TXWY B AND TXWY W; GND CTL REQUESTED WE EXPEDITE OUR TAXI PAST TXWY U FOR TFC FOLLOWING US THAT HAD TO ADHERE TO A DEP SLOT. AS WE PASSED TXWY U GND CTL ASKED IF WE COULD KEEP THE TAXI SPEED UP THE TWR CTLR COULD GET US OUT BEFORE LANDING AN ACFT ON A 5 MILE FINAL. OTHERWISE; WE WOULD HAVE TO GO INTO THE HOLDING/RUNUP AREA AND WAIT FOR THE LNDG TRAFFIC AND ALLOW THE SLOT TRAFFIC TAXIING BEHIND US TO DEPART. WE REQUESTED TO HOLD IN THE RUNUP AREA AS TO NOT RUSH THE TKOF AND DISTURB UP THE PAX. ONCE THE SLOT TRAFFIC WAS CLRED FOR TKOF; TWR CTLR SAID; 'TAXI UP TO AND HOLD SHORT OF RWY 29; TFC ON A 5 MILE FINAL.' I MISUNDERSTOOD THE TRANSMISSION AND THOUGHT THE TWR CTLR TO SAY; 'TAXI INTO POSITION AND HOLD ON RWY 29; TFC ON A 5 MILE FINAL;' AGAIN THE TWR CTLR ATTEMPTING DEPART US BEFORE THE LNDG TFC ON THE 5 MILE FINAL. I CALLED FOR THE RWY LINEUP CHKLIST AND PROCEEDED TO TAXI INTO POSITION AND HOLD. THE FO STARTED TO EXECUTE THE CHKLIST. ALTHOUGH IN RETROSPECT THE FO FOUND IT ODD THAT I CALLED FOR THE RWY LINEUP CHKLIST ONLY BEING CLEARED TO HOLD SHORT. HIS HEAD WAS INSIDE THE COCKPIT EXECUTING THE CHKLIST ITEMS AND BY THE TIME THE FO REALIZED I MISUNDERSTOOD THE CLRNC WE HAD TAXIED PAST THE HOLD SHORT BY HALF THE ACFT. ABOUT THE SAME TIME THE TWR CTLR ASKED IF WE WERE HOLDING SHORT. WE ACKNOWLEDGED AND IMMEDIATELY STOPPED THE ACFT. THE TWR CTLR ASKED IF WE HAD PASSED THE HOLD SHORT LINE AND WE SAID WE DID. AFTER A SHORT PAUSE; THE TWR CTLR ISSUED A GAR CLRNC TO THE LNDG TFC ON APPROX A 3 MILE FINAL. WE WERE SUBSEQUENTLY ISSUED A TKOF CLRNC WITH THE REST OF THE FLT BEING UNEVENTFUL.