Buses start running for character breakfasts @:
appx 6:30am for Magic Kingdom
appx 7:00am for all other parks
You can ask a transportation CM for exact times. Some people on these forums say they start around 6-6:15am for Magic Kingdom.
We caught our bus at SSR at about 7am to get to our Crystal Palace ADR of 8:15am. We stood in line at the breakfast entrance (far right side) for quite a while because they don't let you in until 7:45am. If you can get checked in at Crystal Palace before they open the doors, try to get yourself a picture in front of the castle because it's relatively empty at that point. We checked in a little before 8am (we had to buy autograph books for DD2 and DD6) and got seated with the first group at 8:05am. Even though we hoped to get done with the breakfast by 9am, it didn't happen. We got out about 10 minutes after rope drop, headed straight to Dumbo and had about a 10-15 minute wait already. That was our shortest wait time for the 8-9 times we rode it over 2 days, so if it's on your to do list, do it early. (A few other tips, if you plan to do Goofy's Barn Stormer, get there around rope drop time and you can ride and ride and ride until about 11am when the lines start to form. If you are interested in seeing the Fairies, get to Toon Town Rope Drop before 10am to get in line. We were about 6 families out of being first in line, waited appx 10 minutes to see Tink and friends, spent about 7 minutes with them, and by the time we got out, the wait line was already at 60 minutes. Princesses had a short wait time both days we were there.)
We loved the breakfast. It was our first time there and will be a must do for future trips. You can't beat already being in the park before it opens. Hope you have a great time.