The right equipment helps
While there is nothing wrong with holding your dogs bag of food-rewards or keeping treats in your pockets, it is not ideal when working a class situation. Special purchases are not necessary, an old fanny-pack is fine as is a fishing-style vest that has easy-access pockets. I have even seen a nail or kitchen apron work well. Bags that must be strapped over the shoulder are less ideal.
Many pet stores also carry special bait bags. Some have snap-shut openings, some clip onto belts with drawstrings, and some are worn as a belt. The right bait bag for you will be worn comfortably, allow for you to reach quickly and easily into the opening for rewards and able to be secured so that your dog can not steal treats.