Muggs, you didn't specify if you wanted to use this at home or out on the ice. I just use a cheap aquarium pump and an air stone. Wally World has them cheap.
To keep the air stone on the bottom of the bucket, I tie on a heavy bell sinker, as that takes the hassles out of the air line getting stiff from the cold and pulling up the air stone.
Out on the ice I just dump out half the water in my bucket every few hours and scoop in some fresh water from one of my holes.