The only way I can think of to avoid a bus when leaving MK to get to BW, if Epcot is closed, is to take a cab. If there's another way, someone here will know it!
If Epcot isn't closed & you have park hoppers, you can monorail from MK to Epcot, enter Epcot at the front & walk through to the International Gateway (not a short walk with 3 little ones after a day at the park), then exit at the IG & walk back to BW. We've done this many times when staying at S/D or BC, but not to avoid a bus, just to meander through Epcot, to get a specific snack there, or get 1 more ride in, or to watch Illuminations on our way back.
Good luck!