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 & RB2024 Win.(Audiophile), Sonar Platinum, Cakewalk by Bandlab, Izotope Prod.Bundle, Roland RD-1000, Synthogy Ivory, Kontakt, Focusrite 18i20, KetronSD2, NS40M Monitors, Pioneer Active Monitors, AKG K271 Studio H'phones