Prepare the pieces of mirror or compact disc. If using mirrors, place the glass inside an old pillow case and shatter on pavement using a hammer. With compact discs, microwave the disc for 30 seconds at a time until it's soft enough to be cut into small pieces with a pair of scissors. Either way, create small pieces, roughly the size of fingertips.
Inflate the playground ball until it's fully round and firm using the bike pump (if the ball does not come fully inflated).
Mix the epoxy cement in a disposable container according to the manufacturer's instructions. Mix only a few tablespoons at a time, since this stuff will set up faster than you can use as much as you'll need for the project.
Coat a small portion (about a 2-inch square patch) of the ball in epoxy cement.
Press mirror or CD shards into the epoxy while it's still wet. If working with glass, wear gloves for this portion to protect your fingers from cuts. Place the shards with the shiny sides out into the cement. Cover the patch of cement in this manner, placing the shards as close to each other as possible.
Cover the rest of the ball in the same manner.
Place the finished ball on the bird bath stand. If you like, secure the ball permanently in place with more epoxy.