If your bathroom gets damp you need to deal with the source, mostly likely the shower. When I bought my house it had an extractor over the shower, but the bathroom still got quite damp. I put a second extractor in over the shower, I never get steam any more. The bathroom is super dry, and we only run the extractor for a few minutes after each shower.
A better solution could be a shower dome, which prevents condensation. Some information here. You might still need a small extractor, but maybe not.
Spending money every day to remove water seems silly, even if you do get heat as a byproduct. You'd be better off preventing the moisture, then letting a more efficient heat pump heat that room.
When I redo my bathroom I'll probably have a shower dome, a small ceiling extractor, double glazing, and maybe under floor heating if we go with tiles.