To bemuse is to confuse or puzzle. You could bemuse your teacher by writing an essay as a series of haikus, but don’t. Usually a bemused teacher is not a happy one.
Bemuse is not the same as amuse, which means to entertain someone or make them laugh. If you tell a joke, you don’t want to bemuse your audience because they won’t laugh, they’ll be too busy trying figure out what you just said. New situations and weird dreams bemuse some people, so they feel dazed and bemused.