I have been considering a grey water solution that would achieve two things. The bath in my house is upstairs, and I have an additional toilet downstairs, almost directly underneath. So, I could let the bathwater drain into a tank above the toilet cistern, from where it can slowly release its heat, and then use the water to fill the toilet cistern for flushing. That way, I save on heating and on water usage, and the water wouldn't be evaporating into the house causing humidity problems.
I did the calculations. A 120l bath has water costing £0.53 and heating (by gas, if we assume the incoming water is about 10C and heating it to 40C, about 4.2kWh) costing about £0.44. We probably get out of the bath and drain it when it's about 35C, so if the house is at 22C then there's about 1.8kWh of energy that would get transferred as heat to the house, about £0.19 worth. So, for a very modest cost of installing a tank and a little bit of plumbing (probably less than £200), we'd be saving £0.53 each day (assuming all that water gets used) plus £0.19 each day that we would have the heating on, probably half the year, which is around £230 per year. It'd pay itself off very quickly.
The main concern is that the holding tank doesn't become a bacterial breeding ground, so it may need some chemical discouragement every now and again, but that's hardly difficult.