When I have to put a bar of soap in a soap dish, I still have the same problem: the mixture of water and soap forms a sticky paste in the bottom and I have to rub it to clean it.
This little practical trick will make sure that I will never have this problem again. Here's how:
Install two rubber bands on your soap dish.
Place your soap on the rubber bands rather than in the bottom of the soap dish.
In this way, there will be only a little water that will flow into the bottom, you just have to empty it regularly.