To bumfuzzle is to confuse or fluster. Bumfuzzle is most often used in the dialect of the Southern United States. It is colloquial, meaning it is typically used in informal conversation. It is very similar to bamboozle, and may be derived from it.
Bumfuzzle is used in the South? Really. I've lived here for a total of nearly 30 years and haven't ever heard the word. Nope. Never. Not once. When I saw it, I thought it sounded sort of...Brit!