Is there a plumber in the house?

Lately, when I first turn on the faucet in the downstairs bathtub, a horde (or a hill? a crawl? Just what the heck is the correct affinitive term for them anyway?) of ants comes rushing out ahead of the water. While this is disconcerting, it’s not a big problem in itself–I simply flush them down the drain, like a scene from an insect version of The Ten Commandments, while I’m waiting for the hot water to arrive from the heater.

But I’m worried about the implications of it. Where are they coming from? There’s no trail of ants leading into it, which leads me to conclude that they’re getting into the pipe from somewhere else. That would in turn imply a leak in the system somewhere, but I’ve seen no other symptoms of it. Anyone have any bright (or otherwise) ideas?