Setting aside various mental powers / illusions / whatever, I'd imagine a few days at base. Up to a couple of weeks could be dealt with via makeup (if the BCV knew what it was doing, or had a dominated makeup artist or two), and it'd get increasingly difficult past that point - but would probably never get to the point where a full team of movie costume artists couldn't render it at least vaguely presentable for a few hours at a time.
Edit: But this depends a lot on your definition of how a BCV decays. If they work like a normal corpse, a trained policeman might be able to figure out that there was something wrong in a matter of hours.
