Empty the water from the bird bath. Scrub the surface of the bird bath with water and a firm brush. You may not see a difference at first, but this will remove the top layer of dirt and limescale that is on the bath.
Add vinegar to baking soda until you get a paste-like consistency. Make enough of the paste to cover the stains on the bird bath.
Apply the paste to the stains and allow it to stand for five to 10 minutes. The acid in the vinegar will counteract the minerals left by the hard water.
Rinse the bird bath with water. Make sure not to use the same hard water that caused the stains in the first place.