Yes there is a miniature bull breed but its a miniature bull terrier. It is not really as small as a toy dog though. You can read about this breed here
http://www.minibull.org/
Miniature bulldogs as in smaller versions of the English bulldog are most likely a mixbred dog where the bulldog is crossed with a smaller breed to product pups that are smaller than normal.
They may be crossed with pugs or french bulldogs.
If they have the bulldog heritage they are no more healthy than that breed and may have health issues that the crossing brings with it too.
If you want a smaller bulldog type check into the Boston Terrier, the French Bulldog, and the Pug.
Or if you want a miniature athletic bull breed check into the miniature bull terriers.
Hope this helps you!
Dog Expert:Rescue, Train,Breed,Care
30+ yrs dog home vet care & nursing, rescue, behavior&training, responsible show breeding, genetics