As you probably already know, copyright is complicated. The following sites are promoting themselves as having copyright free music. However, don't take that for granted. You'll need to evaluate each track that you want to use to make sure that it is usable in the way you want to use it.
This archive is a large database of Creative Commons licensed music. However, Creative Commons licenses are given to individual pieces of music by the creators and there are different types of Creative Common Licenses. Therefore, you'll need to look at each track to make sure you can use it for the purposes you intend to. They have some good explanations under their Frequently Asked Questions section.
Many tracks here are licensed for reuse, however there are also many tracks that have been posted without the copyright holder's consent. Be sure that you know who really owns the recording and that person has licensed their work.
This site gives more background information on legal usage, which might help you to better understand how copyright works for the discipline of dance. It also has a list of links to other sites where you can find copyright free music.
The library also subscribes to several music databases where you may be able to use the music for performance.
DRAM: Database of Recorded American Music
DRAM is a not-for-profit resource providing educational communities with on-demand streaming access to CD-quality audio, complete original liner notes and essays from independent record labels, and sound archives. Their primary focus is the preservation and dissemination of important recordings that have been neglected by the commercial marketplace, recordings that may otherwise become lost or forgotten. For more information on copyright and usage see their terms and conditions.
Naxos Music Library [NML] is the world´s largest online classical music library. New CDs are added to the library every month. The library offers the complete Naxos and Marco Polo catalogues plus the complete catalogues or selected titles from over 650 record labels. Music in this library may be used for class sessions, but when it comes to public performances, an individual license will need to be purchased.