My bathroom lock has what you describe. It has a mortise lock with a
deadbolt that is operated by a sort of turnbuckle thingie on the
inside. Otherwise it is similar to the bedroom door locks, which take
a skeleton key.
That being said, in the OP's place I would do as you suggest and just
get a skeleton key to fit, and leave it in the door on the inside. My
recollection, though, is that if the deadbolt is locked from the inside
and the key is still in there, you can't open the lock from the outside
even if you have another key, since the inside key blocks the hole.