What is the name of the black-and-white horror film where a man and women end up at a strange house where a bald man who cannot talk is kept locked up in a room?

I think you might be thinking of two possible movies: either "The Brain That Would Not Die" (1963) or "Spider Baby" from 1964. Both have bald men (one a monster mutation, the other genetically ill) who do not speak and are sometimes locked in a room. Both have a man and woman coming into a strange house. I suspect that "Spider Baby" is more on the mark. It is a creepy little gem.