I tried this once on a cold winter day: I let the bath cool down to room temperature (which was <20C) before letting it drain, with the bathroom door open. The result was a lot of condensation on the windows in the surrounding rooms. I figured the high humidity was going to cause more damage than it saved money, so I scrapped the idea.
It could also be that your windows are not insulated enough. For 20C and 40RH the windows need to be colder then 6C to get condensation.
Either it's being absorbed or you have something removing moisture from the system (venting, etc).