Is it illegal to have a lock on the outside of a bedroom door?

Not unless you intend on locking someone in the bedroom for a long period of time with no means of getting out, and keep them there against their will. In which case, that would be illegal. But, if you just want to keep the room locked and not use the room, then no. The only way something is illegal is if it infringes upon other peoples' rights, or puts them in danger.