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?

Whenever I get something stuck in the back of my throat, I dislodge it by drinking a beer.
It's called the Heineken Maneuver.

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