Is there proof outside the Bible that demons exist?

Yes. You may never have been privy to it yourself, but other people have seen demons or had experiences with them; it is much more common than you think, and we have testimony from credible witnesses. Father Ripperger, for one, can give you stories of his experiences with demons; he actually talks to them and has seen them in different forms. I have heard the same from other priests I have talked to, and nothing I have seen has dispelled those accounts. You are fortunate if you have not experienced it, because it is not pleasant and not something you would want to repeat; be grateful to God that He has not brought you to that. So to answer your question, we have personal testimony from human beings who have encountered demons that yes, they do exist. Where else would they be coming from?