Disney buses are the only transportation allowed near the Magic Kingdom. All buses to the MK leave passengers off at the bus station which is a short walk to the MK entrance. Except for any stops you may have at other All Star resorts your bus will take you directly to the MK entrance.
To get to the Contemporary for the Concourse Steakhouse I suggest when you get off the bus at the MK just take the short walk over. It's about a 10-12 minute walk from the MK entrance to the Contemporary. Starting the walk from the bus station makes it a shorter walk.
If you want you can walk towards the MK entrance and you will see the monorail entrance up the ramp. You can take the monorail one stop to the Contemporary, but the walk from the MK bus station will take less time.