Oh it was worse than just the wood: There was vinyl flooring under the tile, then wood under that, then the subfloor.

Tiles are definitely screwed. I have no hope for them.

Thanks for your input! My intention wasn't to ignore the mold, but to try to seal the leak in the least invasive way. Releasing the spores was one of my main concerns. I'm moderately allergic. But I'm seeing that there's no way around ripping up the floor, even if just to help find the leak and treat the mold.

The rot didn't seem to go too deep or spread far, but very localized. Luckily, the very bottom subfloor seems to have a coating over it that prevented water from affecting that layer.

Very true. Luckily the issue seemed to only appear in the last year or so. The faucet and hardware in the tub wasn't sealed correctly, so I did that, but maybe it was too late at that point. Maybe when I rip up the tile I can see where the dampness is coming from.

That's what I was afraid of. Yay, old houses!