A very small PA system (mixer and two speakers) with a small subwoofer would likely serve you well. EV and QSC have some nice small scale powered speakers that sound great with a small subwoofer, which you will need to get good bass response. Or you could route the bass (from BIAB) through a small bass amp, with everything else going through the small PA speakers. A pair of Bose L1 compact speakers would probably work well too, without a separate subwoofer. I have the Bose "Classic" L1, which would also work OK. I also have a very nice small PA (Tannoy PowerV8's) which I use for everything but bass, which goes through a small Genz Benz bass amp

So far I like the Tannoys with the bass amp best, but this is just my opinion based testing things out in my (fairly large) music room at home. I've played many gigs (keyboard only or singer/keyboard) with both the Bose L1 and my Tannoys. I like the Tannoys a bit better because I can get stereo, which at small venues I think is a plus. At least I like how it sounds better!

I haven't tried out the rig with BIAB at a gig yet, but once I get BIAB gig ready, I'll find out how things sound soon enough.