Taking the bus to the BC/YC (or the BWI/BWV or Swan/Dolphin) is the best way. IMHO, it will take about the same amount of time to walk to Japan from the IG as it would from EPCOT's main entrance, anyway.
I don't recall if the EPCOT resorts always share DD/PI buses or not. If they are sharing when you are there, get off at the first stop if you are in a hurry. That will probably be the Swan. If the buses aren't being shared when you are there, take the first one you see that is going to one of the EPCOT resorts. It really doesn't take much longer to walk from the Swan (farthest from the IG) than it does from the BC bus stop (closest to the IG).
There are no buses FROM DD to EPCOT. IIRC, there are no buses to any of the theme parks from DD. Those routes were discontinued some time ago (because reportedly, most of the riders were DD Hotel guests who used the DD buses instead of the DD Hotel shuttles).