There is no bus from the MK to Fort Wilderness.
The Barbecue is held at Fort Wilderness, not the Wilderness Lodge (very confusing, I know!). To get there from the AKL you will need to take a bus to the MK and then a boat to Fort Wilderness. Once off the boat follow the path to the group of buildings straight ahead and I'm sure you'll see signs for the barbecue.
I would allow a good 60-90 minutes for the transportation. It will probably take much less than that but if your connections are off at all you'll need the time.
Have fun!
Michele