It doesn't look likely that PGM will produce a Linux version, at least not anytime soon.

It is, though, possible to run BiaB on Linux using Wine ... both user pipeline and I, at least, have it mostly working, but there are still a few hangups. Probably the bigbest is that BiaB uses Windows Media Player to play .wma files and that doesn't work for it on Linux. There's a workaround for most things, by expanding the .wma files to .wav, or by getting the audiophile version. The demo songs don't play, I presume because BiaB doesn't even look for a .wav version.

It will also run in VirtualBox on Linux. There's a bit of messing about to route USB MIDI devices.

Have a look through +++ this thread +++ where pipeline helped me to fix a few issues.
My later efforts with +++ AVL:MXE +++ went quite well. I'm now more likely to work with BiaB on Linux than on Windows10, though mostly because I'm a long-term Unix/Linux user.

As an aside, whilst I don't have a huge number of VSTs and similar, most work just fine in Linux, though some of the download managers need some coaxing, for example, the Native-Instruments downloader fails to install downloaded .iso files, but one can just mount and run them manually (there's a special mount mode).

HTH.

Jazz relative beginner, starting at a much older age than was helpful.
Kawai MP6, Korg M50, Ui24R, Saffire Pro 40.
AVL:MXE Linux; Windows 11; Win8.1: Scarletts
BIAB2022 UltraPAK, Reaper, a bunch of stuff.