Hi Jennifer:
I love Chef Mickey's. Every vacation, my boys insist on eating at
Chef Mickey's - for breakfast, dinner, or both. The energy at Chef Mickey's is incredible. My boys not only enjoy the huge buffet, but their smiles shine when Mickey, Donald, Goofy, Pluto, and Minnie stop by the table to pose for pictures and sign autographs.
The
Caribbean Beach Resort does not have a direct bus that will take you to the
Contemporary Resort where Chef Mickey's is located. However, you can hop on a bus at the Caribbean Beach Resort that will take you directly to the Magic Kingdom. Once at the Magic Kingdom, you can stroll along the walkway (about 10-15 minutes) to the Contemporary Resort or hop on the monorail to the Resort. If your breakfast is early in the morning, inform the bus driver that you have reservations at Chef Mickey's. During very early morning bus routes, it's possible the bus driver may be able to drop you right at the Contemporary Resort for your reservation, thereby making the bus route direct.
In terms of how much time to allow yourselves, I'm an early bird. Disney buses are generally scheduled to run on average every 20 minutes from all Disney resorts. The drive to the Magic Kingdom should take about 20 minutes, and the walk or monorail ride to the Contemporary (if you cannot get dropped off in front of the Contemporary) should take 10-15 minutes. So I would budget 50 minutes to an hour. You may arrive early, and if so, you and your 2 and 4 year old can take time to watch the monorail running right through the Contemporary's A-frame main tower and as well as marvel at the lobby's 90-foot, floor-to-ceiling ceramic mural created by Disney Legend, Mary Blair.
Enjoy your vacation.