Stubborn stains in a bird bath are usually caused by chemicals in rain, tap water or well water as well as organic debris. Fill the basin with a quart of water, add 1/2 cup of household bleach, then scrub the basin with a wire brush until any gunk or discoloration disappears. (Use a soft scrub brush rather than a wire brush on shiny ceramic surfaces.) Take care that you don't splash bleach on surrounding vegetation. Rinse well to ensure the bird bath remains chemical-free.