We were at CSR the beginning of March, here is what we encountered. One day around noon time we took a bus to Downtown Disney. This bus was marked "Boardwalk - Downtown Disney". The bus stopped at the BW and then went onto Downtown Disney. It was the same for the return trip back to CSR at about 3:00pm. So this gave us an idea to go to the BW one evening, went to the bus stop @7:30pm and when the bus came, it only said "Downtown Disney", we asked the bus driver and he told us that there are no buses from CSR directly to the BW. He said that we would have to change buses at Downtown Disney. So I guess it depends what time of day you are trying to get to the BW.
I hope this helps.