Bus is definitely fastest (assuming you don't have to wait an inordinate amount of time), but monorail is more fun. My estimate of times is as follows:
Bus ride from MK to Epcot resort area is about 10 - 12 minutes. If the bus still stops at all the Epcot resorts (Swan, Dolphin, YC, BC and Boardwalk), BC would be the fourth stop, which would take another 10 - 15 minutes (to avoid this wait, just get off at the first stop (can't remember if it is Swan or Dophin) and walk to BC (5 minutes) from there).
Monorail to Epcot and then walking through Epcot to BC takes about 45 minutes (assuming there is not a lengthy wait for a monorail). Thus, the extra time is approx. 15 - 20 minutes (which isn't a lot, although there is a lot more walking by cutting through Epcot). We love going this way from MK to BC, but would not do it if we were really in a hurry.