Continue with the auction and get his email address for paypal purposes. Use his email address to look for a Facebook or Myspace account. Then you can at least see if his face looks familiar to you or your neighbors in the area the bike was stolen.

Since it's local, you could always try to do an in-person pickup instead of shipping. Make sure you meet in a parking lot that would have cameras so if anything shady happens it's all on camera. Definitely don't attack the guy, whether he did or didn't steal from you. All that will happen is you will end up in jail too.