A pilot reported a near miss with a BE35 that had entered the pattern from an extended left base and made a 360 degree turn on final to avoid his C172 that was making a visual approach to Runway 28 at FME from the traffic pattern.

Narrative

AS I turned downwind for Runway 28 at FME I stated my position on CTAF. While flying pattern midfield to Runway 28; a Bonanza called Tipton traffic and stated they were on an extended base leg for Runway 28 and to please advise if there was any traffic in the local area. I stated I was abeam Runway 28 and flying downwind. The other pilot stated they did not have us in sight. After a few moments I was unable to find the traffic on extended base leg for Runway 28. The Baltimore Class Bravo is from the surface to 10;000 FT a few miles away from Runway 28. After looking for the traffic; and to prevent entering the Class B airspace I turned base leg for Runway 28. On base leg the Bonanza stated they were on final at 1200 FT. Halfway through the base leg I saw the other aircraft on a 2-3 mile final for the approach to Runway 28. My altitude was 700 FT MSL and both aircraft were on a course that needed attention to prevent a possible mishap. Due to the close proximity of both aircraft and the Class B airspace I was unable to maneuver away from the Bonanza except to turn final. I asked the other pilot if he was going to cut in front of our aircraft? He stated he would do a 360 on final for spacing and be number two for the approach. Both aircraft landed uneventfully. The Bonanza did not enter the VFR traffic pattern as the FAR/AIM recommends. If they entered on the 45; downwind; base and final; the situation would most likely have been better. I have personally seen aircraft converging on final to Runway 28 (FME) a few times and believe this to be a possible safety hazard. Mainly due to the Class B airspace distance to the surface; pilots not entering the traffic pattern as the AIM recommends and number of training aircraft based at FME.