In all honesty your best bet is to take your bowling ball to a pro shop. You will need to get the crack or "hole" plugged. The plug consists of two type of liquids that when combined and let set for 24 will harden to the same hardness as your bowling ball.
In order to patch a bowling ball you have to take it to a pro shop and have them patch and resurface the ball. This is relatively easy, the only downside is usually you will have a miscolored bowling ball. Make sure you polish your bowling ball up after you have this done to ensure proper surface.