Cooking fish in a cooking bag is a convenient, no-mess way to cook fish fully and keep it moist. Clear cooking bags, such as those designed for roasting turkeys, are made of heat-resistant nylon. A foil cooking bag is the safest choice for broiling fish in a bag because of the broiler's higher temperatures and the proximity of the heating element. With a foil cooking bag, you can season the fish and cook it in the same bag.