"Bemuse" isn't a synonym for "amuse." It means to confuse or to occupy the attention of.
Another duo that trips people up is "affect" and "effect."
The verb "affect" means to influence:
Your constant chattering affects my ability to concentrate.
The verb "effect" means to bring about:
If we campaign hard, we may effect change.
The noun "effect" refers to a result:
When I wear earplugs, your noise has no effect on me.