Instead of trying to get from your resort to the BC I suggest you plan on being in World Showcase that part of the day. When it's time to head over to Cape May Cafe just exit WS at the International Gateway. This exit/entrance is past Great Britain. From there the BC is about a five minute walk...just stay to your right.
From there you can either walk to the Studios (about 15-20 minutes) or take the Friendship boats. The boats run from the International Gateway of Epcot to the Studios throughout the day. They stop along the route at the Epcot resorts of Beach Club/Yacht Club (much closer to the YC), the Boardwalk, and the Swan/Dolphin. The boat ride takes as long as walking so if you just miss a boat you might want to walk.
