On my first version 2018 supplied on a HD I just created a BiaB 2018 folder on my external SSD and copied everything from the original BiaB HD in that folder. I opened the app from the SSD, added it to the dock and have had no problems at all. All the updates were installed later on the SSD and have worked right off.

M1 iMac 24” 2021 - Monterey 12.0.1

BiaB UltraPak+ 2021 Mac, (515) + pretty much everything extra.
Yamaha SLG200N - Nektar Impact LX49+ - Logic Pro X - 10.7.1