The hand, arms and forearms are used extensively in bowling so these are good muscles to strengthen. Warm up properly before exercising.
Wrist stretch: Start with one arm out in front of you with your palm facing up. Now with the other hand, grasp the fingers of the outstretched hand and pull towards you stretching the wrist and forearm.
Wrist curls: Sit down on a bench and rest your forearms on the edge. Grab a barbell with an underhand grip and let the bar hang off the edge of your fingers. Curl your wrists towards you and hold it at the top so as to feel the contraction within the wrist flexors. Lower the weight back down to the starting position and then repeat. Go slowly and use light weights.
Overhead triceps extensions: This is to work the triceps muscles often used in bowling. Sit down on a bench and grasp a dumbbell with both hands. Lift the weight overhead and lock your arms at the top pointing towards the ceiling. Keep your elbows pointing up and lower the weight as far as you can behind your head. Then, lift the weight back up towards the ceiling and repeat. You should feel a stretch in your triceps, the muscle behind your biceps.