If you take the bus from WL, you will also stop at the Grand Floridian to make a pick up before going on to Epcot. Depending on when you get to the bus stop and the time of year and day, it could take you anywhere from 20 minutes to 50 minutes.
The WL shares a bus with the Grand Floridian, and the Contemporary shares a bus with the Polynesian. The Port Orleans resorts share busses, The All Star Resorts share busses. The Yacht and Beach share busses and the Swan, Dolphin and Boardwalk share busses.
Those resorts with dedicated bus service may include:
CBR, Pop Century, CSR, AKL, Saratoga Springs, OKW and Fort Wilderness.