Take a bus to the Magic Kingdom.
If you want, you can walk across the MK plaza and get on the monorail to the Contemporary.
If you don't mind just walking, it would take less time to cut a sharp right when you exit the bus stop area and take the walking path between the MK and the Contemporary.
I am assuming that you don't have a car. If you have one, you can just drive to the Contemporary and park there.