Great advice from jlk806.
I think your best bet is to take a bus to DHS and then take the Friendship Boat to the Beach Club. It is actually a reasonable walk (did it a couple of weeks ago), but the boat is more relaxing.
Again, as jlk806 said above, do NOT take a bus to Epcot to get there. You can take a bus to any other park, but the MK is very far away, and the AK isn't close either. Taking a bus to either of those parks will be MUCH longer than going to DHS, which is much closer to the Beach Club.