Call all the shelters in that area. Yes, there are full-blooded animals in shelters. If you do not expect to pay a big price, then probably you don't expect to have to get breeders' papers on the dog. Make a nice puppy happy. Good luck.
For you to find a reasonably priced bulldog or Yorkie in Madison, you can call the dog shelter in that area. If you do not want to pay a bigger price, then don't expect to get breeders' papers on the dog.