Bus from MK is probably fastest because its a short walk from BLT to the bus stops at MK. You'd take the BW resort bus and just walk thru the hotel out onto the boardwalk area. But another option - if you have park hopper tkts - is monorail to EPCOT (resort monorail goes to TTC then get the EPCOT monorail) and then walk thru to Boardwalk (or take the boat from back entrance of EPCOT over to BW).