There is probably an easier way. I’ll get to that in a minute. From what I gather, you want to record the Audio and Midi from you rBB into a DAW. It would be easiest then to have the BB set as the Master, and your DAW as a slave. If the DAW is the master, it is sending clock info into the BB. Midi gets finicky with same piece sending and receiving midi. I assume it might work, but if the BB is the master, then it definitely should work. With the BB set as Master, you would configure the midi OUT setting of the BB to handle your project. Set it as MIDI Out, match the channels, set sync while playing. Set the start to intro or main beat ,depending upon what you want, and set the Stop on Pause Only, Enable notes. Enable Time Signature. Your BB Audio gets sent to an armed Audio track in your DAW and the midi gets sent to an armed midi track.
But, you’ve already created the midi somewhere. Why are you wanting to record it again? IF you have the midi that you put into the BB, just copy and paste that into your DAW. If you used Singular’s parts to create a song, and you don’t have the midi files, you can download them from the Downloads link on the BB’s Product Page (bottom of page, SPECS, FAQ BB vs Competitiion, DOWNLOADS).
You should be able to Export midi from BB Manager, but I understand some versions of BB Manager do this incorrectly. On a Mac, you can control click the song part, and get an option to export midi file. I assume there is a right click function in PC.