CASA212-200 WAS ASKED BY DISPATCH TO REFUEL AND DEPART AS SOON AS POSSIBLE FOR A PRIORITY SHIPMENT OUT OF CLE. DELAYED GETTING CLRNC AND NOTED COMPANY MU2 DEPART TO THE SW. SET OBS OF THE HSI TO SW HDG. CLRED FOR TKOF; MAINTAIN RWY HDG. WHEN AIRBORNE TURNED TO SW HDG. FO MENTIONED MAINTAIN RWY HDG. NO COMMENT FROM DEP CTLR.

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AFTER DROPPING OFF FREIGHT THAT WE HAD BROUGHT TO OSHAWA; OUR DISPATCH TOLD US TO REFUEL AS FAST AS POSSIBLE BECAUSE THEY HAD A HOT TRIP FOR US. MY FO HAD GONE TO GET LUNCH FOR US WHICH LEFT ME TO DO THE FUELING AND FILING OF OUR FLT PLAN. JUST AS I FINISHED DOING ALL THE NECESSARY WORK THE FO RETURNED. I TOLD HIM THAT WE DIDN'T HAVE TIME TO EAT BECAUSE WE HAVE TO LEAVE FOR CLEVELAND RIGHT AWAY. I TELEPHONED OUR DISPATCH AND TOLD THEM WE WOULD BE AIRBORNE IN 10 MINS. I WENT TO THE PLANE AND ASKED THE FO ABOUT OUR CLRNC. HE SAID THAT THE TWR DIDN'T HAVE IT YET AND THEY WOULD CALL US WHEN IT WAS READY. WE WERE DELAYED 10 MINS WAITING FOR OUR CLRNC. DURING THIS TIME WE STARTED OUR ENGS TO AVOID FURTHER DELAY. AFTER COPYING OUR CLRNC; GND CTL CLRED US TO TAXI TO RWY 30. TWR INSTRUCTED US TO HOLD SHORT FOR TFC. WE RESPONDED HOLDING SHORT READY FOR TKOF. WHILE HOLDING; OUR COMPANY MU2 WAS TAXIING FOR DEP AND WAS INSTRUCTED TO HOLD SHORT AT MID-FIELD. AFTER TFC IN THE PATTERN LANDED; TWR TOLD THE MU2 TO TAXI INTO POS AND HOLD FOR RELEASE. WE TOLD THE TWR THAT WE HAD BEEN HOLDING SHORT READY TO GO. TWR RESPONDED THAT HE WAS LETTING THE MU2 GO FIRST BECAUSE IT WAS FASTER. AT SOME POINT DURING THIS TIME I HAD SET MY HDG BUG TO INDICATE SW AS THIS WAS OUR GENERAL DEP. MY STANDARD PROC IS TO SET THE OBS OF THE HSI TO THE DEP AND HDG BUG TO THE RWY HDG. THE TAXI DELAY HAD SET US BACK ANOTHER 10 MINS; COMBINED WITH A 5 MIN TAXI; OUR TIME OFF WAS ALREADY 15 MINS BEYOND WHAT I TOLD OUR DISPATCH. THE COMPANY MU2 DEPARTED AND TURNED TO THE SW. TWR CLRED US TO FLY RWY HDG; CONTACT DEP AIRBORNE. AFTER BECOMING AIRBORNE CLBING THROUGH 1000 FT; I TURNED THE ACFT TO THE SW WHERE MY HDG BUG WAS PLACED. THE FO COMPLETED THE AFTER TKOF CHKLIST; THEN REMARKED THAT WE WERE SUPPOSED TO FLY THE RWY HDG. I IMMEDIATELY TURNED TO THE RWY HDG. THE FO CALLED DEP CTL AND DEP CTL GAVE US A VECTOR TO THE SW. I ESTIMATE THAT OUR POS WAS 3/4 SM FROM THE DEP END OF THE RWY WHEN WE CAUGHT OUR ERROR. ATC MADE NO COMMENTS OF THIS AND THE REST OF THE FLT PROCEEDED NORMALLY. I BELIEVE THAT 3 FACTORS LED TO THIS OCCURRENCE. PRIMARILY BEING IN A HURRY CAUSED ME TO FOCUS ON A SPEEDY DEP INSTEAD OF A PROFICIENT ONE. THE SECONDARY FACTORS WERE GETTING MY HDG BUG TO OUR PRESUMED DEP INSTEAD OF THE TKOF CLRNC; ALSO SEEING OUR COMPANY MU2 DEPART TO THE SW GAVE ME THE MINDSET THAT WE WOULD IMMEDIATELY DEPART TO THE SW. IN THE FUTURE I WILL PLACE LESS IMPORTANCE ON SPD AND MORE IMPORTANCE ON PROPER PROC.