BE35 PLT DESCRIBED CONFLICT AT 4000 FT WITH ACR NEAR BUR WHILE BEING DELAY VECTORED BY SCT FOR SPACING.

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INCIDENT DESCRIPTION: LOSS OF REQUIRED HORIZ SEPARATION BTWN 2 ACFT ON IFR FLT PLANS. APPROX XA40 LCL TIME; I WAS CONDUCTING AN INST CURRENCY FLT IN MY BE-36. I WAS FLYING UNDER THE HOOD AS PIC FROM THE L SEAT; AND MY CFI RATED PLT FRIEND WAS OBSERVING FROM THE R SEAT. INITIALLY; I WAS FLYING E ALONG THE BUR LOC; IN THE INITIAL STAGES OF AN ILS RWY 8 APCH. I HAD BEEN INSTRUCTED BY ATC ON FREQ 134.2 TO DSND TO AND MAINTAIN 4000 FT. WHEN I APCHED THE VICINITY OF SILEX INTXN; I WAS INSTRUCTED BY ATC TO TURN OFF THE LOC IN A DELAYING VECTOR TO THE S FOR MULTIPLE INBOUND JET TFC TO BUR. AFTER A FEW MINS; I WAS THEN GIVEN A VECTOR TO THE W; AND THEN AFTER A FEW MORE MINS THIRD VECTOR TO THE N. MY ALT REMAINED AT 4000 FT MSL. AFTER FLYING THE VECTOR TO THE N FOR A FEW MINS; ATC THEN ADVISED ME THAT THIS VECTOR WOULD CONTINUE ACROSS THE LOC; WHICH I ACKNOWLEDGED. DURING THESE VECTORS OFF THE LOC; I HAD TAKEN OFF THE IFR HOOD TO ENJOY THE VIEW; AND WAS PLANNING TO PUT IT BACK ON WHEN THE APCH BEGAN AGAIN WITH AN INSTRUCTION TO REJOIN THE LOC. HENCE I WAS LOOKING OUTSIDE THE AIRPLANE FOR TFC ALONG WITH MY SAFETY PLT. WHEN ON THE NBOUND HDG; ABOUT 1 1/2 MI S OF THE LOC; I NOTICED A B737 MAKE A ROLLING TURN ONTO THE BUR LOC TO THE W OF US; AT WHAT APPEARED TO BE OUR ALT. AT THAT TIME; IT APPEARED TO BE ABOUT 3 MI AWAY; WITH ALL THE LNDG LIGHTS BRIGHTLY ILLUMINATED AND EASILY DISTINGUISHABLE FROM ONE ANOTHER. I GLANCED AT MY TFC INFO SVC (TIS) DISPLAY ON MY NAV SCREEN AND SAW THAT THE ACFT WAS AT EXACTLY THE SAME ALT AS US. I LOOKED AT MY SAFETY PLT; POINTED OUT THE ACFT; AND SAID THAT THIS 'DIDN'T LOOK GOOD;' AS THE B737 WAS RAPIDLY APCHING US EBOUND ALONG THE LOC AS WE PROCEEDED NBOUND TOWARD THE LOC ON WHAT APPEARED TO BE A CLOSING COURSES. I REALIZED AT THAT MOMENT THAT I WOULD NEED TO INITIATE A TURN TO PUT MORE SPACE BTWN US AND THE OTHER ACFT. I FELT THAT THE BEST CHOICE WOULD BE A TURN TO MY L OR W; ALLOWING THE FASTER B737 TO PASS ON OUR R; AND THEN TURN N AGAIN TO PASS BEHIND IT. AS I BEGAN THAT TURN; MY TIS SYS ISSUED AN AUDIBLE 'TFC' ALERT AND SWITCHED TO THE VISUAL ALERT MODE POINTING OUT THE CONFLICTING TFC IN YELLOW ON MY GARMIN 530 NAV SCREEN. ANOTHER FEW SECONDS LATER; THE ATC CTLR CALLED ME TO ISSUE AN URGENT SOUNDING TFC ALERT FOR THE B737; POINTING OUT THE DIRECTION AND DISTANCE TO THE ACFT AND INSTRUCTING ME TO TURN R. SINCE I WAS ALREADY COMMITTED TO A L-HAND TURN; AND FELT IT TO BE THE SAFER DIRECTION; PUTTING ME BEHIND; RATHER THAN IN FRONT OF THE APCHING JET; I CONTINUED MY L TURN AND TOLD THE ATC CTLR THAT I HAD THE ACFT IN SIGHT AND WAS TURNING L TO AVOID IT. A FEW MOMENTS LATER; THE JET PASSED TO OUR R SIDE AT A DISTANCE OF LESS THAN 1 MI. AFTER THE JET HAD PASSED; I TURNED BACK TO OUR ASSIGNED NORTHERLY HDG; CROSSED OVER THE LOC; WAS THEN VECTORED IN 2 R TURNS ONTO THE LOC AND THEN COMPLETED THE ILS 8 APCH INTO BUR. DURING THE ENTIRE INCIDENT; WE REMAINED LEVEL AT 4000 FT MSL. IT DID NOT APPEAR THAT THE B737 JET TOOK ANY EVASIVE ACTION; IT NEITHER TURNED; CLBED NOR DSNDED; BUT CONTINUED IN LEVEL FLT TRACKING THE LOC. SUPPLEMENTAL INFO FROM ACN 711495: BOEING DSNDED THROUGH ASSIGNED ALT OF 5000 FT. BE36 AT 4000 FT TOOK EVASIVE MANEUVER TO AVOID B737.