As for how they identify you: there's a few different methods. One they use is actually using BT and recording the IPs, then reverse mapping them. Another is to use packet sniffing and traffic shaping. Encryption of BT traffic doesn't encrypt the full stream, only portions of the traffic, hence it's still identifiable. Your school may also be doing port scans--if a BT client answers, well there you go.
About the only way you can be sure you're not back tracked is to use an VPN as is being offered by Relaks, an encrypted proxy (like Tor), or similar.
In your case, you know the school is doing something--find out what, exactly. Make some friends in the schools computer labs, they'll have their ears to the ground. Adapt your methods accordingly. See if your public library (not the school's) has wireless, and use that. Check to see if there are other open public wireless networks in your area.
Ultimately, though, you have to decide if the risk is worth it.