I totally agree with Jack's post but there's just one point I'd add to it, where Jack said "Ask yourself, honestly, if your dog is way above average in at least 2 major categories (Gameness, Stamina, Durability, Athleticism, Intelligence, Mouth, Finish)"
I would add this if a dog has is way above average in any two of these areas or even 4 or 5 of them but does not poses gameness then I wouldn't breed from the dog, I take gameness almost as the most important foundation in any line of bulldogs.

I'm not saying we can not breed from a dog that hasn't been checked and tested but I do believe that if a dog is proven to be not game then it should not be bred from it should be culled or if for some bizarre reason you love the dog and can't bring yourself to cull it then neuter it so it can never do harm to the breed by being bred from.