I used to work at an allergy office and was tested while I work there and had a mild positive to dogs. All I kept saying was I don't care, I'm getting a bulldog! (This was probably about 3 years ago!) I usually don't have problems with Hudson. Sometimes I get a rash on my arms after we play a lot, but I have TONS of contact with him and I don't vacuum much....so I guess I'm doing okay.
Pet allergies are really interesting because often people will be tested and have a positive reaction to animal in their home that they've never had problems with. (especially with cats) For whatever reason, people tend to build up against their own pets, but have problems with others.
The best solution to see how tolerant you are is to actually spend a day in someone's home who has a Bulldog to see how you fare. Then just take reasonable precautions in your own home. Bathe the dog regularly, keep him out of the bedroom, and limit contact if needed.
However, for someone really reactive, it's probably better never to establish that bond and then have to give them up. It's just a judgement call, I guess. Best of luck!