If its only vaguely similar to what you basically described as the breath of a cigarrette smoker, it could be that the bathroom was fairly regularly smoked in for a while, like multiple months or a year, and then the smoking stopped, and either a bit of time passed, a few weeks or months, and/or some kind of chemical was used to try to mask/remove the cigarrete odor baked into the walls.

That would then be ‘like smoker breath, but a bit off’.