There is a way to make a satisfactory Bm without a barre (similar to the grip for a 4-string, 3-finger F chord).
- Fret the high E and the B with the pad of the index finger fret 2
- Fret the B (also) with the middle finger fret 3 (I'll explain below)
- Fret the G with the little finger fret 4
- Fret the D with the ring finger fret 4
- Fret the low E with the thumb fret 2 and also mute the A with the thumb (This is optional. If you don't do it then just play the four high strings.)
I use two fingers on the same string in this chord for a couple of reasons:
1. Your grip is more secure when you fret both the high E and the B with the index (as opposed to just the E), and
2. This particular grip will allow you to alternate between Bm and Bsus2 simply by lifting the middle finger. (Example: the bridge in Bob Seger's "Mainstreet".)
I often find that techniques I learn or discover for myself, while they may not be the "right" way to do something, work just fine, and make my guitar playing more enjoyable for me. I'm not planning on being a pro, so if I find something that works I'm not too much of a purist to use it.