LJ45 CREW HAD 2 TCASII EVENTS ARRIVING AT BED.

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BOSTON APCH GAVE US A DSCNT TO 3000 FT MSL AT LOBBY; AND TO EXPECT THE VISUAL APCH TO RWY 23 AT BED. WE WERE HEADING APPROX 75 DEGS DIRECT TO LOBBY. PASSING THROUGH 4500 FT MSL; OUR TCASII GAVE US A TA ON AN ACFT BELOW AND TO OUR R AT 1.5 MI. THE TCASII RESOLUTION DIRECTED US TO DSND AT 1200-1400 FPM TO AVOID THE TFC. I TOOK THIS ACTION AT THE SAME TIME THE CTLR INSTRUCTED US TO CLB TO 4000 FT MSL. SIMULTANEOUSLY; THE PNF ACQUIRED THE TFC VISUALLY; AND TALKED MY EYES ONTO THE TFC. THE TFC WAS XING R TO L ON A NORTHERLY HDG. I IMMEDIATELY PULLED TO THE R (S) SO AS TO LAG THE COLLISION COURSE AND FURTHER INCREASE THE LATERAL SEPARATION ALONG WITH THE TCASII COMMAND FOR VERT SEPARATION. THE VISUAL EVASIVE ACTION ACTUALLY SHALLOWED MY DSCNT TO LEVEL FLT; AND WE PASSED BEHIND THE CESSNA BY APPROX 550-1000 FT LATERALLY; AND SLIGHTLY HIGH ON THE FLT PATH. IT IS OF INTEREST TO NOTE; THAT AS MY FLT PATH SHALLOWED OUT BY MY VISUAL MANEUVERING; THE TCASII COMMANDED AN IMMEDIATE CLB. I WAS IMPRESSED WITH THE PERFORMANCE OF THE TCASII TO THIS FLUID MANEUVERING/ENVIRONMENT. NO PRIOR WARNING OF TFC WAS GIVEN TO PREVENT THIS INCIDENT BY APCH CTL. IF THIS HAD BEEN A TRUE IMC OR NON-VISUAL EVENT; I BELIEVED THE TCASII WAS CORRECT FROM MY SIGHT PICTURE; AND THE COMMANDED DSCNT WOULD HAVE TAKEN US RIGHT UNDER THE CESSNA WITHOUT INCURRING A COLLISION. THE XING ANGLE WAS A TRUE COLLISION COURSE; AND WOULD HAVE PLACED US DIRECTLY UNDER THE CESSNA'S FLT PATH. FROM MY EXPERIENCE IN FLYING FIGHTERS IN THE USAF; THIS WOULD HAVE BEEN A DEFINITE VIOLATION OF THE RULES OF ENGAGEMENT 500 FT BUBBLE. WITH THE PROX OF THE ATC HDOF TO BEDFORD TWR; I WAS NOT ABLE TO TALK WITH THE CTLR AND TO INFORM HIM THAT WE MANEUVERED OFF TCASII. I THINK FROM HIS REPLIES ON THE RADIO AFTER THE INCIDENT; THAT HE; TOO; KNEW IT WAS A CLOSE ENCOUNTER. TCASII TRAINING PAID OFF. FOLLOW THE COMMANDS. THE FIRST THING THAT FLASHED THROUGH MY MIND AS THE TCASII COMMANDED ONE DIRECTION AND THE CTLR DIRECTED ANOTHER; WAS THE MID AIR IN GERMANY LAST YR. MY PNF DID A GREAT JOB ON VISUALLY ACQUIRING THE TFC; AND CONTRIBUTED TO INCREASING THE MISS DISTANCE THROUGH GOOD VERBAL DIRECTIONS. HE WAS PREPARED TO TAKE THE EVASIVE ACTION VISUALLY IF I HAD NOT DONE SO; AND I HAD NOT VERBALIZED MY ACTIONS TO HIM AT THE GIVEN MOMENT. HIS HANDS WERE 'RESTING' ON THE YOKE. AS WE APCHED BED; ON THE EXTENDED R BASE TO RWY 23. WE FLEW RIGHT OVER THE TOP OF A MOONEY THAT WAS ON THE R DOWNWIND TO RWY 23. THE ATC TWR CTLR WAS OVERLOADED WITH DEPS; ARRS; AND VFR PATTERNS. WE WERE ADVISED BY TWR OF THE TFC AT THE LAST MIN AND AVOIDED THAT CONFLICT VISUALLY; WITH THE AID OF TCASII TFC CALL. THIS WAS MY FIRST TRIP TO BEDFORD.