If you'd like your sand dollars to be whiter, or you're having trouble cleaning them with water alone, you may consider using bleach. Mix equal amounts of bleach and water. and gently place your sand dollars into the solution.  If you're cleaning a number of sand dollars, fill a baking tray with the bleach-and-water solution. This will allow you to spread a number of sand dollars evenly over a broad surface. Make sure that there's enough solution in the tray to cover the entire sand dollar. You can also use a bowl, a bucket, or a Tupperware container. If you're only cleaning one sand dollar, find a small bowl, lid, or other container. You won't need much bleach to get the intended effect. Be careful not to soak the sand dollars in bleach for too long: the shell will begin to soften and disintegrate if it's left in too strong of a solution. If you want to soak the shells for a longer period, reduce the bleach concentration. Be careful when handling bleach. Don't get bleach in your eyes, and don't swallow the solution. Wash your hands with soap after any contact with bleach. Move the sand dollars from the bleach solution into a bowl or tray of fresh water.  The bleach may continue to disintegrate the shell even after you've removed the sand dollar from the solution. Rinse the bleached shell thoroughly in fresh water to neutralize the bleach solution and remove any remaining dirt. When you're sure that the sand dollar is clean, leave it out to dry. Within a few hours it should be ready to decorate, display, or store as a keepsake. Sand dollars will harden over time, but you should continue to handle them carefully. This may come in handy if you plan to use if for craft projects, or if you want to display it without worrying about breaking it.  Mix together equal portions of water and white craft glue. Use a sponge brush or a paintbrush to completely cover the sand dollar with the mixture. Let the shell dry, and the glue solution will harden like a glaze. Sand dollars will harden naturally, over time, the drier they become. Bear in mind that thicker glue mixtures may conceal some of the natural texture of the shell. Once your sand dollar is hardened and dried, it's ready to use or display. You can paint or decorate your sand dollars, give them as gifts, or display them as they are.

Summary:
Soak the sand dollars in a bleach solution. Rinse after bleaching. Consider hardening the sand dollar with glue.