We started showing our dogs through the National Kennel Club (NKC) and then branched out to the ABRA to give us more options for shows closer to home.
I talk to a lot of new American Bulldog owners who show a curiousity about showing their puppy/dog. It's a fun way of getting together with other American Bulldog owners and learning more about the breed and even about your dog.
Most registries sponsor their own shows and each has its own written standard. A standard is a description of the "perfect" American Bulldog. Their height, weight, shape, color, length of tail and even their ears are all addressed in the standard. You can find the NKC and ABA standards under the ABD info tab. The purpose of a dog show is to find the dog who is closest to the standard.
I would recommend that every American Bulldog owner attend at least one dog show for the experience.