I'm assuming the OP will have no car there, otherwise I don't think the question would have been posed. Your own car is always fastest in a situation like this.
The best case scenario w/o a car, though, is definitely the bus. We've done the BC to MK via the EPCOT monorail before, and let me tell you, that took FOREVER! 1 hour and 45 minutes to be exact. Keeping in mind you have to wait for 2 different monorails, then ride them for 10-15 minutes apiece, you also have a VERY long walk from the front of EPCOT to the IG exit. Budget a good 15-20 minutes of walking, more if it's crowded.
The direct MK to BW resort bus is much, much easier and faster, even if it makes a stop or two at other EPCOT resorts. I will agree with some other posters, though, in that you could probably exit the bus at just about any of the EPCOT area resorts and have a not-so-bad walk to the Boardwalk from there.