AN LJ60 CREW; DEPARTING JYO; VIOLATED IAD'S CLASS B AIRSPACE.

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IN PREPARING TO DEPART JYO RWY 17; WE CONTACTED IAD CLRNC FOR OUR IFR CLRNC. WE WERE GIVEN SUBSTANTIAL RTE CHANGES FROM OUR FILED ROUTING AND A RELEASE TIME WITHIN 5 MINS EVEN THOUGH WE HAD NOT YET STARTED ENGS. I DECLINED THIS RELEASE WINDOW AND WAS ISSUED A RELEASE THAT EXTENDED OUR RELEASE WINDOW BY 3 MINS. DEP INSTRUCTIONS INCLUDED A R TURN DIRECT MRB AFTER TKOF. I STARTED ENGS AND BEGAN TO TAXI WHILE MY FO LOADED THE FLT PLAN INTO THE FMS AND SET THE AVIONICS. WE ARRIVED AT THE END OF THE RWY WITH 1 MIN LEFT IN OUR RELEASE WINDOW. WE QUICKLY ACCOMPLISHED THE BEFORE TKOF CHKLIST AND TOOK OFF ON RWY 17 (JYO). THE FO WAS FLYING. CLBING THROUGH 1000 FT ON THE WAY TO 3000 FT; I CONTACTED IAD APCH CTL. THE CTLR RESPONDED THAT HE HAD RADAR CONTACT AND WE CONTINUED OUR CLB TO 3000 FT. SHORTLY; THE CTLR DIRECTED AN ACFT (NOT OUR CALL SIGN) TO TURN 330 DEGS. HE THEN ASKED OUR HDG. I RESPONDED '171 DEGS.' HE THEN AGAIN DIRECTED A 330 DEG HDG (NOT OUR CALLSIGN; AGAIN). THE CTLR THEN DIRECTED THAT WE CORRECT OUR IFF CODE AND DIRECTED THAT WE TURN TO 330 DEG HDG. WE COMPLIED WITH HIS DIRECTION. AT THAT TIME; WE WERE 7 MI S OF JYO. AT NO TIME DID WE CONFLICT WITH OTHER AIR TFC (NO TCASII WARNINGS). OF THESE CAUSES; RUSHING TO GET AIRBORNE WAS THE MOST SIGNIFICANT AND CONTRIBUTED TO MOST OF THE OTHER FAILURES.