Bulldogs can be prey driven animals...I would never trust the dog and the bird alone. Now if you introduce them as soon as you get the pup and train him that the bird is off limits, the two could be in the room together while supervised. Just remeber..it would require alot of training and diligence on all involved.
If the training is too much work, maybe see about caging your bird for periods of time when the dog will be out..or keeping the two in totally separate rooms.