I know that it is important to be aware of live music and/or bands when shooting events, and the use of that music in video reproductions. (like a highlights video)

So, do any of you have a short document/form that you can get signed by the band/musician giving you permission to use their music in your final video?

Chris the only thing you would have to concern yourself with is if what was performed is original content where the performers also hold copyright on the pieces. If they were doing "covers" of someone other artist's work, that would then be a need for a license from the copyright holder(s) to use those work(s) in your production.

If they were original pieces, look at Creative Common licenses that would apply for your use and request that from the artist.