You would have to take the bus to the park that has MEMH and then get to the WL from there. Magic Kingdom will only work if your reservation on a Thursday. Then the bus may not start until 7:30am, if the park opens at 8 for MEMH. Then with 30 minutes I am not sure you will make it. If memory serves you have to take a bus from the boat launch at WL to get to the lodge, or it is a hike.
I would cab it over there for ~$10 and use transportation to come back.