Originally Posted by
sole leisure
Fair Use is a tricky subject. Even if you bought the song, you don't have the rights to use it in a project, non-profit or not. Plus, BMI or ASCAP are unlikely to respond or give you the rights to use it. The Fair Use doctrine is a defense that allows you to use copyrighted material for the sake of education or parody. For example, if you're shooting a documentary and you want to show a few clips of Kanye West's songs, you can probably get by under Fair Use. Something that is NOT fair use would be using Can't Tell Me Nothing as background music for your action movie.
Under normal circumstances, you're unlikely to get caught, but if your professor is hard on that type of stuff, then you're better off making your own songs or finding a band to make some music for you.
If you're really interested, here's a comic that explains Fair Use, but it's pretty long.
http://www.law.duke.edu/cspd/comics/zoomcomic.html