From the closest cabins (not counting the like 2 cabins that you almost never can get) it is almost precisely a one mile walk to the spot where the bus would drop you off. Could you make this in 20 minutes? Yes, if you are walker ad you don’t dally. But you are on vacation!
I normally walk every day back and forth to work, about 3/4 of a mile, 15 minutes each way. I would not even consider walking as a general method of transportation inside Fort Wilderness. I’ve said the same thing as you before but when actually presented with having to walk around that place every day, maybe multiple times a day, I always back down.
The busses normally run often enough that they would be passing you if you were making the walk. Its just in the very early mornings before park open that they seem to be less frequent.