If you transfer MIDI back and forth, you will always have MIDI and it will play with whatever MIDI-player you have or in the program. I think transferring from BIAB to MuseScore will not help you much, if at all.
BIAB's forte is in creating accompaniment for songs, based upon the chord progressions that you give it.
It's important with BIAB to differentiate between MIDI tracks and RealTracks. You can supply MIDI tracks to BIAB and it will play them through a MIDI-player like a soundfont player, or with a VST instrument. Or more usually, you would supply BIAB with the chord progressions and BIAB will generate the MIDI for you. The playing process creates the audio, of course. With RealTracks, what BIAB does is use segments of pre-recorded playing by real musicians, using phrases that match the chords you supplied. BIAB uses some wizardry to make this remarkably smooth and realistic. Note, though, that as a rule RealTracks are not MIDI, they're audio, so you can't transfer them to another MIDI program(*), only to an audio program.
(*) There are some variances/exceptions to that, but they're too complex to worry about for now.
If this has piqued your interest, try listening to some of the songs on this website in the "User Showcase" forum, and to some of the songs made by Henry Clarke.
If you decide to try BIAB, there's no trial version, you need to order a version, but PG Music are good about a refund if you choose to cancel. There's also a "gotcha" that often causes confusion, in that the version called "Pro" is the entry-level version. It comes with a modest number of styles and RealTracks. Most people, sooner or later, get the UltraPak version, which comes with a huge amount. Curiously it's usually slightly cheaper to start with the Pro and upgrade than to start with the UltraPak. It's then not an insignificant amount of money, but if you use the RealTracks instead of VSTs, you would save on the latter, so it may work well for you.