I don't know the answer for sure (we did our first BLT trip last year but had a rental car). I have to think its the Contemporary since you have to check in at their front desk??
Most all buses stop at the porte cochere at the Contemporary. You will have to check in at the front desk of the Contemporary, so the drop off there will be very convienient.
You check in at the Contemporary. There is no check-in desk in the BLT lobby. DME will drop you at the Contemporary entrance. If you need luggage services, Contemporary bell services will assist you.