As with any allergies, it would depend of the severity of the person who is allergic. If you are highly allergic to dog dander, unfortunately you will have to not have a dog. (sad thought really....)
Since Bulldogs are mainly indoor dogs, this could be a real problem, as bulldogs cannot cope in heat or extreme cold.
It will also highly depend on the owners care for the dog in question.
I do not think Bullies are as bad as other dogs, especially if you have them on good food and NuVet vitamins. Making sure they are cleaned with good shampoo and on a regular basis is important. In other words, the better you care for your dog the less problems you (both) will have....