Here is an article from a reader who wants to share his own experience with his dog. I think this is valuable information and helps us to understand our dogs (and cats) a lot better, and helps us to promote harmony in the home when you have cats and dogs together.
This is from David Brow:
The dog I own is a Bull Terrier cross breed. With this breed of dog their temperament is all about how you treat them, especially when they are puppies. The sad fact is that there are some people who just use these dogs as fighting animals and think that they're right in doing so. The truth is that the Bull Terrier can be a very emotional dog and sometimes can be temperamental and persistent in getting their way, but you can assert control with(out) having to resort to aggression towards them.
Like cats, hitting a Bull Terrier does nothing. I believe these dogs were originally bred for pig hunting, yet they are not the vicious killers as people claim they are and I have known a few people who have bull terriers and cats together. I think that the Bull Terrier can sometimes get over-affectionate with a cat and they have been known to show signs of grief when the cat is gone. Another thing is that they are protective of the family that owns them, even a cat from other cats, but that from the observation from my own dog with my friend's cat who was living with me for 5 years.
As with the Jack Russell Terrier, it is true they aren't all tolerant of cats, but that seems to be a common trait with all the Terrier breeds, but I think that is because they are more of a 'one owner animal' and once you have adopted one as a pet, which you would have to get as a puppy, as an older Terrier tends to grieve for its original owner, and you would have to accept that this type of dog is for life. You can assimilate both cat and Terrier but you can't force them and both pets will eventually get used to each other.