SMA ON INST APCH HAS SMA APPEAR UNDER R WING. NMAC.

Narrative

AT APPROX XA45Z; ON AN IFR CLRNC; HAVING BEEN CLRED TO W FIELD VOR RWY 20 APCH AT 2100 MSL AND 1 NM OUTSIDE KLYDE INTXN; AN SMA A APPEARED UNDER THE R WING OF MY ACFT. I INFORMED THE BRADLEY CTLR; EXECUTED A 360 SHARP R TURN FOR SEPARATION; TOOK MY STUDENT OFF THE HOOD; CANCELLED MY IFR CLRNC AND CONTACTED THE W FIELD TWR. UPON COMPLETING THE TURN I NOTED THAT THE SMA A WAS DIRECTLY AHEAD AND AT MY ALT 1900 FT. I THEN FOLLOWED THE SMA A MAKING A STRAIGHT-IN APCH TO RWY 20 W FIELD. WHEN CLRING THE RWY I NOTED THE SMA A; WHITE WITH RED MARKINGS; NUMBER XYY. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES HE CALLED APCH AFTER LNDG AND GOT NO SATISFACTION REGARDING SITUATION. INFORMED THE OTHER PLT WAS VFR AND HAD RPTR ACFT IN SIGHT. IF TRUE PROX WAS MUCH TOO CLOSE FOR RPTR. EXTREMELY STARTLING WITH NO WARNING. CTLR STATED HE HAD A TRAINEE AT THE TIME AND DID NOT WANT TO TAKE OVER TOO SOON. THIS IMMEDIATELY LED RPTR TO QUESTION JUST HOW CLOSE DO WE HAVE TO GET? RPTR HAS FRIEND IN FAA WHO SUGGESTED HE FILE ASRS RPT.