The buses start running, every day/every resort, by 6:30am. But, with that being said, you still may have an issue with an ADR that early. You would have to be out at the bus stop no later than 6:15 in order to be on the first bus. When you board the bus, ask the driver which is faster, walking or monorail to CR..that you have an ADR at 7:05. The driver 'may' offer to drop you right at the CR, either on the way to MK, or on the way out. But, that isn't something you should count on.
If the driver doesn't offer to drop you, get off the bus, and stay to the right as you head to MK. You will see a sidewalk that runs directly beneath the overhead monorail line. Follow this to the CR..it takes just under 10 mins to walk it.
My issue is that you have to be on the first bus..otherwise, another may not be along until just before 7am. Even if you get on the first bus, you may not get to MK until close to 7 and you need to be at the podium at CMs by 6:55ish.
If you don't want to stress about it, take a cab directly to the CR around 6:45.