When I broke my wrist and was in a cast, I found that plastic bags taped over it so I could shower were such a pain and a hassle, that I went to a medical supply store to see what they had that could make my life easier.

I got a water tight sleeve that just slipped on and off, and it was a godsend. Just Google Seal-Tight Cast Protector and you'll find lots of places where you can purchase them. They have them for arms and legs, and in different lengths.