Evidently the drippy leaky problem happening in the bathroom with the tub is a separate issue. We haven't quite gotten that one figured out yet, but it's much less of a problem now that I know it's not soaking the basement.
I pulled up the wet carpet in the basement and I've got my beloved box fan on it. I hope I can sleep without my fan.
The only bad thing about this is that we don't get/need to remodel the tub and shower now. *shrug* I suppose that's a good thing since I can't really afford it at the moment anyway.