
Hi Max! Bull terriers, like many other breeds which can be predominantly white (boxers, dalmatians, English setters etc), can suffer from hereditary deafness, and a reputable breeder will have all pups, whether white or coloured, BAER tested before sale, and will not sell you a totally deaf puppy. Those who are deaf in one ear can still hear perfectly well enough (probably better than you or I) to lead a completely normal life - in fact in most cases it is impossible to tell the difference between a dog with full bilateral hearing and one who can only hear in one ear.
Dogs with white ears and muzzles can suffer from sunburn in the summer, and ordinary sunblock on these areas will prevent that. There should be no need for many vet checks at all - the 'hundreds of vet checks' bit is indeed a load of rubbish.
Hope this helps.