Hi Cara!
Thank you for bringing your question to the Disney Parks Moms Panel!
Since the
Magic Kingdom is scheduled to open at 8 a.m. on June 3, 2016, the buses from your resort should begin running about an hour, to an hour and a half prior to 8:00. I would be hesitant to rely on a 7:00 a.m. bus to get me to that reservation. My first suggestion is to stop by your front desk the day before your meal at
Chef Mickey's to get a better idea of what time they expect the buses to begin running that next morning. If you feel like it's early enough (I would want to be on a bus by no later than 6:45), then you would take the bus to the Magic Kingdom. Once there, I recommend walking on the path to the Contemporary Resort. You could also take a monorail, but there is a nice path from the Magic Kingdom to the Contemporary that is about a ten-minute walk. I believe that would be faster than the monorail because of wait times and lines.
My absolute first choice would be to arrange for a cab or an Uber car. I used Uber several times on my last trip. It was very inexpensive and easy to use from the phone app. Your front desk can also arrange for a cab to pick you up. I think you could travel there for around $10 in a cab. I hate being late for things, so that would be what I would do!
I hope this helps! Please let me know if you have any other questions.