Yes, there is a difference — a big difference. The two words are not synonymous, as some people believe. When something “amuses” an individual, it makes him laugh or smile. He finds it funny or entertaining.
Example: The principal found the comments made by the students very amusing.
“Bemuse”, unlike amuse, has nothing to do with making people laugh. When you are “bemused” by something, you are bewildered by it. It leaves you confused or puzzled.
For example, when the stranger walked into the classroom, the children looked at her with a bemused expression.