When you go from A to B variations within a style, is it possible to keep the drums in A only? The reason is that on many styles that I use, the B variation provides a snare hit that’s way too loud for my tastes. I don’t know how to tame that and don’t won’t to get into editing. Most of the time, the A drum variation will work fine throughout the tune.

If you are using RealDrums, you could play the entire song with the A substyle (variation), then freeze the drums track, then change the part markers to B wherever you want the other instruments to play the B substyle and regenerate the song and save it. The drums would stay with the A substyle throughout the entire song because they're frozen while the other instruments will play whatever you have selected using part markers.

If you are not using RealDrums, I think you would have to open the song in RealBand and make the changes there, but I'm not sure how do to it. I can't comment on that because I don't use RealBand (yet - maybe someday).

There may be a control somewhere in BIAB to do what you want. It's been years since I've seen it (if it indeed exists). Try unchecking "Vary style in middle choruses". If your song can fit in the BIAB limit then one long track will stay in substyle a. For instance a 32 bar tune can be written out 4 times with no change in style.
Check out "substyles" in the help-index menu.

Very good suggestions on things I didn’t think of. Many thanks. As a follow-up comment on the original post (and especially if anyone from BIAB reads these posts), I’d like to suggest that future style developers pay close attention to the final mix and how the various instruments interact with each other---especially volume levels across variations. I find that playing live with BIAB, it’s often difficult to keep things in balance going from style to style, despite my own efforts at mixing. For example, you can’t put the bass on 90 and expect it to be right for each style and song played. There’s a lot of variation at times, especially between Real and midi tracks. One might think that if BIAB can employ all these great players to create Real Tracks, they might consider employing professional mix/mastering personnel (those with the golden ears) to help put the final polish on new styles. Just an observation. I love BIAB. Been with it since the earliest days.

As of version 2016, you can specify 'no fills' for drums at part markers. Otherwise I would do it the way Jim says, freezing the track.