Jolene:
If your breakfast reservation begins after Epcot opens, you can simply take a bus from the Art of Animation Resort to Epcot and walk to the back of the park and over to the Beach Club where
Cape May is located. However, my guess is that you may have an early breakfast reservation before the park opens, hence, the question.
If you are relying on Disney transportation only, you will need to take a bus to Downtown Disney and then transfer to the bus to
Beach Club. Give yourself a good 45 minutes to an hour for this ride. But honestly, considering the short distance and the option of a VERY long walk or bus wait, it might be worth the taxi fare as the ride is about 7 minutes in a car. It is always worth asking the concierge when you check in if they would provide complementary transportation, but that is not guaranteed.
Wishing y'all a magical vacation!
Whitney