AN A300 CAPT RPTS THE AIRPLANE WAS DISPATCHED WITH A #2 ENG BLEED INOP. PRIOR TO DEP; THE APU FAILED AND WAS DEFERRED. MUST HAVE APU OPERATIVE WITH FAILED BLEED.

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ON ARR AT THE RAMP; ACCOMPANIED BY THE STUDENT FO WE GOT THE WX; CHKED THE FPR; NOTED #2 ENG BLEED VALVE WAS DEFERRED. REVIEWED MEL AND ACTIONS REQUIRED TO COMPLY WITH MEL. PROCEEDED TO ACFT X TO BEGIN PREFLT. IT WAS THE FO'S FIRST TRIP; SO WE ACCOMPLISHED THE EXTERIOR INSPECTION. THE INTERIOR INSPECTION; HAZARDOUS CONTAINER INSPECTION; AND JUMPSEAT BRIEFING; AS WELL AS MY NORMAL COCKPIT PREFLT. THE PACE WAS RATHER HECTIC AND DURING COCKPIT SET-UP; THE MECH TOLD ME THE APU HAD AUTO SHUTDOWN AND WOULD BE DEFERRED; AND WE WOULD HUFFER START BOTH ENGS. WE CHKED MEL FOR AUTO SHUTDOWN AND THE MECH PROVIDED US WITH TIME AND INITIALS FROM OPS CTR FOR OUR RELEASE. I DID NOT XCHK THE APU MEL AGAINST THE #2 BLEED MEL SINCE I HAD CHKED IT EARLIER. WE STARTED BOTH ENGS IN THE BLOCKS; PUSHED BACK; AND FLEW UNEVENTFULLY TO ZZZ1. BOTH OUR MAINT OPS CTR AND OPS CTR HAD RELEASED THE ACFT AND I HAD ASSUMED IT WAS OK. THE ACFT WAS SUBSEQUENTLY GNDED IN ZZZ1. WHEN IT WAS DISCOVERED THAT #2 BLEED MEL STATED THAT TO DISPATCH WITH IT DEFERRED; THE APU BLEED MUST OPERATE NORMALLY. THE ULTIMATE RESPONSIBILITY WAS MINE BUT MAINT OPS CTR AND OUR OPS CTR SHOULD HAVE CAUGHT ERROR BEFORE RELEASING THE ACFT. HAD I RECHKED THE BLEED VALVE MEL I WOULD HAVE CAUGHT THE ERROR; BUT BY THE TIME THE APU WAS DEFERRED; WE HAD BASICALLY FORGOTTEN ABOUT THE BLEED VALVE. COMBINATION OF EVENTS; IE; NEW STUDENT; FIRST TRIP; HURRYING TO COMPLETE OUR REQUIREMENTS; GET OPS CTR APPROVAL AND PUSH BACK ON TIME; THE MISTAKE WAS MADE.