The main walkway emerges from Epcot's International Gateway, passes a bridge over to the Boardwalk, passes the BCV, then continues along the shore past the entire BC and YC. It's not a "private entrance" by any means, but it's a wonderful way to duck out of Epcot after IllumiNations.
There is a smaller, more private walkway that might be the one you're thinking of. It starts at the edge of the BC closest to Epcot as a little gated branch off the main walkway, and winds along the "woodlands" past the Epcot side of the BC and the BCV. Taking this to the main path makes it possible to avoid going out through the BC lobby, which is actually in the wrong direction when you're trying to get to Epcot.