Having had this happen before, here's how I handled it:
Had a guy walk in asking questions about Kenpo, and how it stacked up against other arts. He was full of questions, and was letting on that he hadn't studied "much" in the past, a little here and there. After talking with him for a while, I realized there was more to that story. Eventually, I found out that he had reached blue belt in one karate style and something like yellow in a grappling style. I started to suspect that he was a belt collector, looking to impress people with the number and variety of arts he had studied. After talking with him a little more, I found out that this was not the case.....he had bad experiences with other arts, and was honestly looking to find one he liked. However, he was very tentative in asking questions and revealing much, due to the excessive sales pitches he had received, instead of answers.
He eventually signed up for an intro program at our school and liked what he found there. However, he had to move after a couple of months, and had to leave the school (moved out of state). During his stay, he was an excellent student, and was very curteous.
Hey, if you have an idiot coming in just wanting to prove himself, let him......if he is doing that, the only thing he will prove most often is what a goon he is. But be aware.....guys coming in just to "challenge match" should sign a waiver....the last thing you or your school needs is a lawsuit.
Oh, yeah.....and don't be taken in by the "bully". Let him talk, and if he wants to sign up for classes and challenge the big boys, well......at least he's been warned. If he proves to be all talk, then all he's wasted has been your time.
Peace--