Depends on your plans for the day and your type of park tickets! If going direct from CBR, there are many ways:
1) As previous poster mentioned, bus to DHS and boat to BC (no park admission required);
2) Bus to DHS and walk to BC (no park admission required);
3) Bus to Epcot and walk through Epcot/out International Gateway to BC (requires valid park admission and an open Epcot); or
4) take a cab.
If we were going direct from CBR to BC, we'd probably just take a cab. But we usually make our resort dinner ADRs coordinate with our park plans for the day. So if your Cape May ADR is at the end of an Epcot day or a DHS day, you could just boat or walk over to BC for dinner and you save a lot of transportation time.
On the way back, a cab is always an option. Otherwise, you'll have to watch park hours to make sure you can get through Epcot to the bus to CBR (park admission required) or that the buses from DHS are still running.
P.S. You could always drive if you have your own car - but we rarely do - so I always forget about that option!