However, when practicing a chord progression on your own, it's helpful to isolate the difficult transitions. It sounds like you've already identified a problem area for yourself, so the next step would be to focus on that specific transition (A to Bm).
If you slow things down and really take the time to see what you're left hand is doing, you may find more efficient ways to bridge the gap. A lot of this will happen over time of course, as your hands acquire more "muscle memory" for the chords in question.