We had one in our old house. I suppose it wouldn't be a problem for your bully to use it.
That being said, I would be concerned about one thing. SUMMER. We know how our bullies love to sun bathe even though they shouldn't spend so much time out when it is hot. I think during the warm months, I would lock it to make sure they don't stay out so long. Some of them might know when to come in, but one of mine surely doesn't! lol. The rest of year, I think it would work perfectly!