As the other respondents have stated, there is no formal walking path or sidewalks between the two. For wahtever reason, the property was not designed for non-motorized vehicle traffic between resorts/parks/other amusements.
That said, you have a a bit of a hard choice- walk where you were not meant to walk, take a bus to Epcot and walk through to the back entrance over to the BW or take a quick, yet relatively expensive cab ride if you don't have a rental car.
I, myself, would walk to the BW and maybe hop a cab back. I have run around the Epcot Resort area and it is difficult but do-able.