Carpenter ants are bigger than these. Also, there are some nice web pages (like this one at UMN) that seem to indicate that I'm not looking at carpenter ants.

Nonetheless, given that they're swarming into my shower, it's almost certainly the case that moisture from the shower is getting into the wood behind the shower and they're nesting back there (ant larvae apparently like moisture). The cheap answer is to get an exterminator to pipe poisonous dust into the wall. The expensive answer is to tear out and rebuild the shower.