Cut a hole in the ice and use a garden hose. Put one end in the hole and hang the hose over a net. Suck on the other end until the water starts to flow. The water will keep coming as long as you keep the end of the hose lower than the top of the net. It's a million times easier than using a bucket. The mop idea is a good one, though.
Oh, and don't put the hole too close to the rink. Any snow on the ice will press the ice down and water will seep out of the hole until the hole freezes. If the hole is right next to the rink, this could overflow onto part of the rink ruin your nice smooth surface.