Sounds to me like a bodge job by an electrician which, as often happens, takes a while to manifest itself: Sounds as so the shower and light are on the same circuit/spur. I don't know about the US, but here in the UK, we have separate lighting and power circuits, but both things often end up on a lighting circuit.

It took me years with my shower, clearing up damp, to figure out that the extractor fan had been put in upside down and was blowing steam around the bedroom!