Truthfully the quickest way to do this is to take a cab for about $10. But if you want to do Disney transportation you have 3 options.
1. Take bus to Epcot, enter main gate and walk through FW and WS and exit out the International Gateway. Then keep walking straight to BC. Or you can take a boat from the International Gateway, but this is a waste of time if the boat is not there waiting for you.
2. Take a bus to MGM and then either walk(which is a pretty good hike), or take the boat to BC.
3. Take a bus to MK or AK (whichever comes first) and then take the bus to the YC/BC.
You will need to plan some time for all three of these options, because you never know how long you will have to wait for a bus or boat. Most things I have read, have said to plan at least an hour to get from resort to resort with Disney transportation.