Hi Erica and welcome to the Disney Parks Moms Panel.
Firstly, let me start by saying that in all of my family's visits to the Walt Disney World Resort, we have never once experienced any problems in using Disney's
Complimentary Resort Transportation to get us to early morning Advance Dining Reservations.
In actual fact, my family just returned from a 2 week split stay at Disney's Coronado Springs Resort & Disney's Caribbean Beach Resort a couple of weeks ago and were able to catch buses to the Magic Kingdom Park as early as 7:00 AM from both Resort hotels on days when the Magic Kingdom Park was not scheduled to open until 9:00 AM.
Anyway, back to your question. On the day of your breakfast reservation at
Chef Mickey's, you will need to take a bus from your Resort hotel to the Magic Kingdom Park and then from there, take a short 5 minute stroll over to Disney's Contemporary Resort. As your Advance Dining Reservation is for 8:00 AM, I would recommend that you be at the bus stop at your Disney Resort hotel by no later than 7:00 AM.
To be on the safe side, I would recommend that you stop by the Front Desk at
Disney's Caribbean Beach Resort prior to the date of your Advance Dining Reservation at Chef Mickey's to ensure that the buses will be running early enough.
Wishing you a magical trip filled with memories which will last a lifetime!
Emma