At the latest. These early morning buses run less frequently than regular buses. If you arrive at the bus stop and the bus is just pulling away, it could be close to 7 by the time another bus comes.
Note that the buses run to the theme parks- not the resorts. Take the bus to MK and walk over to the Contemporary. If you mention to the bus driver that you have an ADR at CM, you might get lucky and get dropped off at the Contemporary.