A C-T210 PLT TURNED THE WRONG WAY DURING AN IFR DEP FROM TVC.

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I WAS ON AN IFR FLT PLAN FROM TVC TO BIS. THE WX AT TVC WAS VFR (VISIBILITY 10 MI; CEILING 5000 FT). THE TWR GAVE ME MY CLRNC; AND THEN CLRED ME FOR TKOF ON RWY 10; WITH INSTRUCTIONS TO TURN L ON COURSE. MY ENRTE COURSE WAS 290 DEGS. AT ABOUT 500 FT; I BECAME UNSURE WHETHER I HAD BEEN INSTRUCTED TO TURN L ON COURSE; OR TO TURN R ON COURSE. TURNING L ON COURSE WOULD PUT ME DIRECTLY OVER TOWN AND IT SEEMED MORE LIKELY THAT I WOULD HAVE BEEN TOLD TO TURN R. I CALLED TWR AND ASKED 'WAS THAT A R OR L TURN?' I GOT NO ANSWER; AND I STARTED A TURN TO THE R. I DID NOT MAKE A SECOND ATTEMPT TO CONTACT THE TWR. A MIN OR 2 LATER; AFTER I WAS ALREADY IN THE CLBING R TURN; I WAS INSTRUCTED TO CONTACT UPON CONTACTING CTR; THEY NOTED I HAD TURNED R INSTEAD OF L; AND IT TURNED OUT THEY HAD A INBND ACFT (COMING FROM THE WE AND A LNDG ON RWY 10; I BELIEVE). AS FAR AS I KNOW; AT NO POINT WAS THERE A TFC CONFLICT. AT THAT POINT; MY RECOLLECTION OF WHAT WAS SAID IS HAZY. I CONTINUED MY TURN TOWARD THE W; AND A MIN OR SO LATER; CTR THEN ASKED MY HDG -- 'TURNING THROUGH 260 DEGS TO 290DEGS.' APPARENTLY; AFTER THE INITIAL CALL TO CTR; THEY HAD TOLD ME TO TURN TO A HDG OF 120 DEGS; BUT I DO NOT REMEMBER THAT CALL; AND AM FAIRLY SURE I DID NOT ACKNOWLEDGE SUCH INSTRUCTIONS. AT THAT POINT; CTR TOLD ME TO TURN TO 360 DEGS; AND LEVEL OFF AT 2000 FT. THAT PUT ME OVER THE ARPT. SEVERAL MI N OF THE FIELD; I WAS TOLD TO TURN L ON COURSE AND CLB TO MY CRUISING ALT. CTR ALSO MADE CLR THAT THEY WERE UNHAPPY THAT I HAD NOT FOLLOWED INSTRUCTIONS. THEY ASKED IF I HAD RECEIVED TWR'S 'TURN L AFTER TKOF' AND I CONFIRMED THAT I HAD. I MENTIONED MY ABORTED ATTEMPT TO GET CLARIFICATION FROM TWR BUT THEY DISMISSED THAT. IN REVIEWING THIS INCIDENT; IT IS CLR THAT I GOOFED IN NOT TURNING L. I SHOULD HAVE INSISTED ON A RESPONSE FROM TWR WHEN I QUESTIONED THE 'L OR R' INSTRUCTION. ALTERNATIVELY; GETTING ON RESPONSE FROM TWR; I SHOULD HAVE CONTINUED ON A RWY HDG AND ASKED CTR WHAT THEY WANTED M TO DO RATHER THAN MAKING THE ASSUMPTION I DID. FATIGUE PROBABLY PLAYED A PART SINCE I HAD ALREADY FLOWN 3 AND A HALF HRS FROM THE BALTIMORE AREA; IN IFR AND TURBULENT CONDITIONS. ALSO; THEY RELATIVELY GOOD LCL WX (5000 FT OVERCAST AND 10 MIL VISIBILITY); AND APPARENT LACK OF OTHER ACFT; DULLED MY VIGILANCE. WITH RESPECT TO THE INSTRUCTION TO 'TURN TO 120 DEGS;' I REALLY HAVE NO EXPLANATION OTHER THAN MY MIND WAS PROBABLY OCCUPIED WITH THE 'WHY DID YOU TURN R WHEN YOU SHOULD HAVE TURNED L' REBUKE FROM CTR.