Doing a slow transition is so their tummy doesn't get upset from the difference in ingredients in the old and new foods. It basically is feeding 1/4 new food mixed with 3/4 old for for about a week, then mix 1/2 and 1/2 old and new for another week. Then 3/4 new food and 1/4 old food for another week before feeding 100% new food. Along the way, if your bullie starts to get loose poo you may want to back up a little on the mixture for a while longer before preceding.
Also, I had a discussion with a rep from Earthborn and he said that whenever he transitions from one food to another he adds a couple tablespoons of canned pumpkin to the mix. Said he never has a soft poo issue doing it that way. Hope this helps.