The Posterior chain and core are particularly important in bowling. Big compound moves such deadlifts, squats, pull ups , pressing exercise (military or bench) are your best bet to improve general strength and improve body composition which will also assist you. Ballistic exercises such as kettlebell swings and Olympic lifts can improve power output which means you can use your gained strength more effectively in a sporting environment (no good being able to bench/squat x number of kilos if you do it in a slow manner not applicable to sports) however olympic lifts can be dangerous if done with incorrect technique so you should seek a coach for this and stick to easier to learn variations such as with kettlebell or dumbells as opposed to traditional barbell. Isolation exercises such as bicep curls are a waste of time in my opinion. There are various ways to train your core from your basic planks to loaded carries (e.g farmers walks).
As suggested by others bands and calisthenics are other potential avenues of training you could look to and of course actually performing the skill of bowling at nets etc!