The others are correct, it is not going to happen. Probably the fastest way would be to take a bus to Saratoga Springs and then walk to Downtown Disney- but with all the construction, I'm not even sure of the status of the walking paths. I think Saratoga also has a boat and a bus, but I'm not sure how much time that will add. You can walk to the Contemporary and take the bus to Downtown Disney, but be aware that after leaving the Contemporary that bus typically stops at the Poly and then the GF before going to Downtown Disney. It has taken us over 30 minutes to get to DTD from the Poly with the stop at the GF- so it could be even longer from the Contemporary, and that is not counting the time you have to wait for the bus, or to walk there. You could walk over to CR and take a taxi, but that is going to cost you. You could take a boat to the GF and grab a bus- at least you would be the last stop before DTD- we have waited 30 minutes for DTD buses at the GF though more than once- not that it would probably be any better at the Contemporary. Also, BOG is in the back of the park though, so it is going to take some time just to get from there to the front of MK. We quit going to DTD altogether, because it always seemed like it took forever to get there and back. You would need to be leaving MK about 12:20- the time of your reservation, to be sure you were going to make it over to DTD in time for the appointment.
I would keep trying every day to get your BBB moved to MK. If your DD doesn't know about it, or if it isn't her top priority, even if you can't get an MK appointment, I would cancel the DTD appointment if it is on your MK day. You are going to lose way too much MK time out of your day going back and forth.