I'd have to re-read; I just don't remember clearly enough to have a firm opinion as to whether Bob does or doesn't know...
Pretty effective I believe, plus Alfred scared the living crap out of Bob.
I don't think Bob would be very eager to go back to the island. Without the Warden accompanying/avouching him... completely unwilling (modulo the "have to obey the owner of the skull" bargain).
That doesn't mean Bob might not divulge the info to someone other than Harry, if he were in said "someone's" possession...
But I don't think that simply "having the password" is sufficient to bypass Alfred's active defenses, it just "lowers the drawbridge" in some passive ones.