Dogs are natural chewers, and a dog that chews on his bed is generally doing so either to fight pain or to keep his jaws strong. According to the ASPCA, dogs also chew in response to boredom or to relieve frustration and anxiety.
Destructive chewing can also be an attempt by the dog to alleviate hunger, as dogs will chew objects that smell like food or that are related to food, like a pet dish or a bone. Puppies that are teething also seek out things to chew on.
Keep in mind that chewing is natural for a dog. Keeping a dog from chewing up his bed may be as simple as giving him some type of chew toy to divert his attention from his destructive behavior.