Instructions
Put yourself between the ball and its direction of travel. Depending on the size of the ball, you may want to reconsider. If it appears as though the ball will hurt you, use a pillow.
Hold the ball in place. The ball is technically still moving with the orbit of the Earth on its axis and its movement around the sun, but for argument's sake, let's assume the ball isn't moving anymore. At the very least, it isn't bouncing.
Wait for the ball to stop bouncing out of its own goodwill. Eventually the kinetic energy of the ball will run out and it will succumb to the force of the Earth's gravity to rest in place. This is an opportunity for you to grab some water, in anticipation of tracking down and stopping the another bouncing ball.
Smother the ball with a blanket. You can either keep the blanket in your arms as you hold it apart, or you can throw the blanket, like a net, onto the bouncing ball. This is similar to netting a kangaroo.
Close your eyes. Open them in 10 seconds and the bouncing ball will likely have stopped. You might not know where it is, so listen. If you don't hear any bouncing, it has likely stopped moving.