I can't see any reason that BB could not exist on an external drive. That is essentially the main way to do it for the Audiophile version.
You will need to run the installer to get fonts and things setup.
But you just run from the X:\bb folder (where X is the external drive).


BIAB & RB2026 Win.(Audiophile), Windows 10 Pro & Windows 11, Cakewalk Bandlab, Izotope Prod.Bundle, Roland RD-1000, Synthogy Ivory, Session Keys Grand S & Electric R, Kontakt, Focusrite 18i20, KetronSD2, NS40M, Pioneer Active Monitors.