FWIW - I do most all of my work in my DAW, Studio One Pro 6 and I work in MIDI most all of the time. But if I ran into a problem like this here is what I would do:
1-get the song exactly as I want it while ignoring the bass problem.
2-move the entire song to my DAW
3-back in BiaB raise the base track up an octave - note I have my DAW in ASIO and BiaB in MME - thus both can be open simultaneously
4-move the raised base track to my DAW.
5-cut and paste the bass line to my satisfaction

I know this may or may not help as it just what I would do.

However I believe you should put a suggestion in the wishlist forum. I can see a big benefit for those whom work in BiaB with RTs.

PS - I have a question. Does the base sound OK raised an octave? I would guess there would be some sound problems raising it that amount. Or is the base buried in the mix so those artifacts are noticeable?

My goal this weekend is to move just enough each day so that no one pokes me to see if I'm dead or not.

64 bit Win 10 Pro, the latest BiaB/RB, Roland Octa-Capture audio interface, a ton of software/hardware