[MMM]

I think it is easy for people to mix up public bath houses and hot springs. As a tourist, he probably won't be going to a public bath...but a hot spring would be a different story.

The bath house is just that, a local public bath. Everyone needs to get clean, so tattoos aren't going to scare people off. Hot springs are more expensive, and are tourist destinations, so keeping them quiet, civil and problem-free is in the owners' best interest. You can't say "No yakuza" so that problem is resolved with "no tattoos".