DBF thought it was a loose bottom bracket too, but I *think* I fixed it.

I think it was a loose bolt on the saddle clamp thing, combined with a slightly loose rear wheel. I double checked that after I got home (tightened things up a bit more), and then tightened up the bolt on the clamp (since I needed to adjust the saddle tilt anyway), and took it for a little spin, and haven't heard a peep out of it since.