How do you pick the right size bowling ball?

The only way is to go to a local Pro Shop. Usually you can find this in your local Bowling alley, but if you have choices as to which alley to go to, your best bet would be to ask friends or anybody you know that bowls competitively and they may be able to recommend you to a good proshop owner.

They will specifically measure the span from your thumb to your middle and ring finger, and the diameter of each finger. If you get someone good they can also measure your hand (or watch the way you already bowl) to determine the correct pitch to use for your thumb.