Take the Animal Kingdom Character Breakfast Bus. They are dispatched every 15 mins from 7:00am-8:00am, and can take you directly to AKL. After 8:00am, take the Animal Kingdom theme park bus, and transfer.
It took us roughly an hour to get from Yacht Club (which is right near Dolphin) to AKL for a dinner at Jiko - be sure to allow more time than you'll think for travel time. (we had to change busses at Downtown Disney)
Thanks very much. This was the deciding factor in us renting a car. We could do the parks without one, but I don't want to spend two hours commutting for dinners and breakfasts. (and my husband insists on doing Boma at least once for each). I'm off to find a cheap rate on a rental car!