If we had Midi UserTracks we could do this all in Biab but we don't at the moment so I'll show you another way.
This is using Reaper with ReaTrak.
So what we will do is create up a midi drum style that will instantly be fitted to the Biab Chords/Part Markers.
ReaTrak will fit them with the following action buttons:
1. Select Track
2. Choose Instrument
3. ReaTrak Selection
4. or Redo Selection

to try this there are a few Test Instruments & Drums HERE

To create up a Midi Style Drum track we just drag the sections out of Jamstix/EZDrummer/MT Power Drummer/DrumMic'A.. into a Reaper track with snap enabled.
I had the Free version of Jamstix so I couldn't DRAG the phrases out so I set the Jamstix track in Reaper to Record Midi Output, armed it and hit record, this gave all the Midi phrases in a midi track.
Put a time selection the length of the section item then Shift+R to insert a region,
The count-in/intro is 2 bars
fills 1 bar
endings 4 bars for BB (or more if you stay in Reaper)
so you need to select the bar of a post fill or fill and Shift+R,
we then color that region by having the cursor under it and hit the correct Section Color Action button.

we then select all the midi phrases and glue them,
you can then double click the consolidated midi item,
in the Midi Editor Ctrl+A select all notes right click a note and set the channel to 10 or what you want.
File > Export project MIDI, Selected item Time selection,
save midi with "Drums" in name in a folder
Drums, Rock Jamstix 01 Ev8 4-4 120bpm
and in that folder
Drums, Rock Jamstix 01 + Riffs Ev8 4-4 120bpm.mid
hit "Export/Renumber Chords" or export in Region Manager
Drums, Rock Jamstix 01 + Riffs Ev8 4-4 120bpm.csv

This is a basic Midi Drum Style you would add more variety of playing, more count-ins/intros, more endings and more riffs to make a better one.
This is in Jamstix mapping:
Drums,_Rock Jamstix_01_Ev8_4-4_120bpm.zip.mp4 ** Note remove the .mp4 and open the zip.

To open the demo Midi Drum Style, in ReaTrak hit "Import Chords" button or Reaper Region Manager import region csv, then drag the midi in.

To get your chords from Biab to Reaper you can use the Biab Plugin or Export to MusicXML (for older versions) that is dragged into Reaper then hit "MusicXML Chords" you will need to split/color the regions manually.
If you are using the Biab Plugin in Reaper,
make sure the chord sheet is unfolded in the SGU or open the SGU in the Biab Plugin and down the bottom right, click the arrow to unfold,
now Save the SGU and Re-Open it !!
hit the "Biab Plugin Chords" button.

Now you have the chords and part markers in Reaper,
Set Jamstix to MIDI PLAYBACK,
set the time selection to the whole song or just the section you need,
1. Select Track
2. Choose Instrument eg. Drums, Rock Jamstix 01 + Riffs Ev8 4-4 120bpm.mid
3. ReaTrak Selection
4. or Redo Selection
When done you can glue the track and import to Biab and set Jamstix, EZDrummer etc.. as the VSTi, hopefully soon we will have midi drag drop import to the piano roll.
You could also render to audio first then drag drop the wav into the Audio Edit window with Snap enabled (don't run BB as Admin for drag n drop to work)

Now if you want to change sections:

ReaTrak Biab & Plugin in Reaper
Free Biab Chord Picker Tool