If the "bathroom" portion of the OP's question is a shower room and there is a lot of high humidity present, and... the OP is located in a warm climate where lots of air conditioning is involved, you might find that there is more energy saved by simply exhausting the moist air than removing the moisture from the air via the A/C evaporator handling the latent heat of the water vapor in the air.
Do the calcs. They are eye-opening.
I spent most of my life resenting anyone in my household exhausting air that I had paid cold hard cash to heat or cool. Then I got involved in a project at work with a Hx that takes humidity out of air at various operating conditions and when I saw the duty required to do the condensing (as opposed to the sensible air cooling), I am now the one that insists that the vent fan is run when anyone showers.
rmw