There is no way I would book an ADR at that early time unless I was either staying at that resort, or at a nearby resort from which I could walk. So...with that in mind....get a cab. There is a very good chance you won't make it to the CR in time.
Yes, the buses start running at 6:30...that means you have to be out at the bus stop by 6:15...sometimes the buses run a bit early. If you miss that first bus, you aren't making it. And yes, sometimes the driver will drop you at the CR, either before or after the MK drop. But...it isn't a sure thing. I always ask the driver, when I board the bus, what the quickest way to the CR is..walking or the monorail. The driver may offer to drop you off...or he may simply give you the info you requested...and then head to MK where you will have to find your way over to the CR. This is what happens more often than not.
And add to that the fact that the monorail doesn't start running until 7...you will have to walk from MK..takes about 8-10 mins depending on your pace.
And the idea of calling down to the front desk, or concierge, to find out about bus timing??? Don't do it. They have no idea. I have asked the front desk, or what I thought was the front desk, what time the buses start running. I have almost always been told...'About an hour or so before park opening'. I have found resort CMs to be less than helpful, or even close to accurate, when talking about transportation issues.
I would just take a cab. It will be worth the price. You can leave your resort at about 6:40 and get dropped right at the CR. So much easier than worrying about timing and buses.