A C172 HAS AN NMAC WITH A BE V35 IN BJC; CO; AIRSPACE. C172 PLT TAKES EVASIVE ACTION.

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THE LCL CTLR ISSUED NO TA'S TO ME WHILE I WAS ON AN APPROVED TRANSITION THROUGH HER CLASS D AIRSPACE. IN ADDITION; I HAVE HAD PREVIOUS PROBS WITH THIS PARTICULAR CTLR; SUCH AS INABILITY TO UNDERSTAND HER ON THE RADIO; AN ATTITUDE THAT SHE IS ALWAYS RIGHT AND YOU ARE ALWAYS WRONG; SHE GETS VERY CONFUSED A LOT OF THE TIME. I INITIATED AN APPROX 1000 FPM DSCNT TO AVOID THE COLLISION AND THE OTHER ACFT PASSED 75 FT OVER MY HEAD. FACTORS I FEEL CONTRIBUTED: 1) CTLR WAS PREOCCUPIED WITH AN ACFT ON HER RWY THAT HAD BLOWN A TIRE; BUT WHICH WAS STOPPED ON THE RWY. 2) CTLR'S INABILITY TO DIVIDE ATTN BTWN GND OPS AND AIR OPS. 3) I WAS SCANNING BUT OBVIOUSLY COULD HAVE DONE BETTER. I PICKED UP THE BONANZA ONLY APPROX 2-3 SECONDS BEFORE COLLISION. 4) LACK OF COM BTWN LCL CTLR AND MYSELF (AND THE OTHER PLT). WAYS TO SOLVE: 1) MORE EFFECTIVE SCANNING BY ALL PLTS INVOLVED. 2) LESS PREOCCUPATION BY CTLR TO THE ACFT WITH THE BLOWN TIRE. 3) BETTER ATC SUPERVISION OF A CTLR WHO IS OF QUESTIONABLE ABILITY.