PA28 ARR TO BLI; INSTRUCTED TO FOLLOW P3 ON STRAIGHT IN APCH TO RWY 34; EXPERIENCED NMAC WITH CESSNA ON DOWNWIND.

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ON INITIAL CONTACT WITH BELLINGHAM TWR 10 MI SE FROM THE FIELD; THE TWR CTLR INSTRUCTED ME TO RPT 3 MI SE AND TO EXPECT A R TURN WHICH WAS AN UNUSUAL INSTRUCTION FROM WHAT I HAD EXPECTED (L TURN FOR A STRAIGHT-IN FOR RWY 34). I READ BACK THE INSTRUCTION AND PROCEEDED TO DSND FROM MY CRUISING ALT OF 2500 FT FOR THE APCH. A SHORT WHILE LATER; THE CTLR ADVISES ME THAT A P3 WAS COMING IN ON A STRAIGHT-IN APCH FOR THE ARPT AND FOR ME TO RPT HIM IN SIGHT. I LOOKED TO MY 7 O'CLOCK POS AND SAW THE P3 ABOUT 3 OR 4 MI BEHIND ME ON APCH TO RWY 34. I ACKNOWLEDGED THAT I HAD THE P3 IN SIGHT. I WAS ABOUT 6 OR 7 MI SE OF THE RWY AT THIS POINT AND THE CTLR INSTRUCTED ME TO FOLLOW THE P3 AND TO REMAIN WELL E OF THE CTRLINE FOR RWY 34. I ACKNOWLEDGED HIS INSTRUCTION AND CONTINUED WITH MY APCH TO THE ARPT AT A REDUCED SPD SO THAT THE P3 CAN OVERTAKE ME ON THE L. A SHORT WHILE LATER; AN INBOUND CESSNA; THAT THE TWR HAD BEEN IN CONTACT WITH; RPTED THAT HE IS ENTERING THE DOWNWIND FOR RWY 34. THE CTLR ACKNOWLEDGES THE CALL AND INFORMS THE CESSNA THAT HE IS #3 TO FOLLOW ME. THE CESSNA PLT ACKNOWLEDGES THE CALL. MY POS THEN WAS ABOUT 3 MI SE OF THE RWY AND THE P3 IS AT MY 8 O'CLOCK POS AND ABOUT TO OVERTAKE ME ON THE L. AT THAT TIME THE RADIO BECAME BUSY AND I COULD NOT GET IN A CALL TO INSTRUCT THE TWR THAT I WAS ABOUT TO BEGIN A R 270 DEG TURN IN ORDER TO GET BEHIND THE P3. AT THAT VERY MOMENT I SAW THE CESSNA THAT THE TWR HAS BEEN IN CONTACT WITH ON A WIDE R DOWNWIND FOR RWY 34 APCHING ON MY R AND EVENTUALLY PASSING BELOW ME BY A COUPLE HUNDRED FT. THIS SURPRISED ME AS RWY 34 IS NORMALLY L DOWNWIND. THE CTLR THEN QUERIED THE CESSNA FOR HIS POS AND THE PLT RPTED THAT HE WAS ABEAM THE P3 WHO IS NOW ON A 1 MI FINAL. THE CESSNA APPARENTLY DID NOT HAVE ME IN SIGHT. THE CTLR THEN ASKS ME FOR A POS RPT AND I RESPONDED THAT I AM APCHING THE SHORELINE AND THAT THE CESSNA JUST WENT UNDERNEATH ME. THERE WAS SOME MOMENTARY CONFUSION AND THE TWR THEN INSTRUCTED THE CESSNA THAT HE'S NOW #2 TO FOLLOW THE P3. THE CESSNA PLT ACKNOWLEDGED AND THE TWR THEN INSTRUCTED ME TO FOLLOW THE CESSNA. I ACKNOWLEDGED THE INSTRUCTION AND MADE A R 270 DEG TURN TO FOLLOW THE CESSNA. WHEN I WAS FINALLY ON A LONG FINAL FOR RWY 34; THE TWR QUERIED ME WHY I DIDN'T FOLLOW THE P3 AS ORIGINALLY INSTRUCTED AND I EXPLAINED THE SITUATION TO HIM AND HE RESPONDED WITH 'I THINK I SEE WHAT HAPPENED THERE.' IN RETROSPECT; I DID NOT ADEQUATELY MAINTAIN A FULL SITUATIONAL AWARENESS OF THE CESSNA'S LOCATION RELATIVE TO THE ARPT AND MY ACFT IN THE CLASS D ENVIRONMENT. I WAS EXPECTING THE CESSNA TO BE ON A L DOWNWIND ON THE WESTERN SIDE OF THE ARPT AND DID NOT VERIFY WITH THE TWR THAT THIS WAS THE CASE. I SHOULD'VE INQUIRED ABOUT THE CESSNA'S LOCATION RELATIVE TO MINE WHICH MAY HAVE ALERTED ME TO REACT SOONER INSTEAD OF WATCHING THE P3 OVERTAKE ME ON MY L. I PROBABLY SHOULD'VE EXECUTED THE R 180 DEG TURN SOONER SO AS TO PUT MYSELF ON A VERY EXTENDED R DOWNWIND RELATIVE TO THE P3 AND AHEAD OF THE CESSNA.