Do you know any of the triggers? A lot of bullies are allergic to Chicken and do not react well to grains. I've been using Taste of the Wild with Bison and Boris has been doing well on it. He has issues with Chicken, Turkey, salmon and potatoes so we've been on an adventure moving him to an adult food that doesn't cause him to react. There are a lot of folks here that like the Fromms 4 star kibble since you can easily switch between the proteins without having to phase them into the new kibble.
Here's a link to the rating board on EBN:
English Bulldog News Forums - Dog Food Ratings at English Bulldog News
best of luck!