What tempo -approximately, does the issue start to present at? i.e. 130bpm and above, or?

Is there a chord, progression, or chords in particular you changing from which presents this problem, or is it any change?

What guitar are you using? solid body electric, steel stringed acoustic, wide necked classical?

In the case of the first two, what gauge strings (relative to tension), and is your action set to spec or lower, or, if you can't answer the last question, when did you last have your guitar checked or serviced.

I play Bm almost every day in songs, using multiple voicings. Some songs entirely barre chords others a mix of both, others all open. I may be able to help/ have a solution for you once I know more about the circumstances where you're encountering this issue.

P.S. ...a few minutes later. Having just dragged out my acoustic for confirmational self analysis of my own fretting to be certain, I already have one suggestion where I can see a potential obstacle you appear to be creating for yourself, but will save further mention of it until I have more info about [u]your[/u] specific circumstances.