Sometimes, Disney runs a bus to the Boardwalk from CS. That's because CS is a convention hotel and many of its guests visit the Boardwalk. Check with the front desk at CS. If there's a direct bus, that's you best option. As you probably know, it's only a short walk (maybe 5 minutes) from the BW to the Swan.
If it were me, I'd take a cab rather than take the bus from CS to DD and transfer there to another bus going to the Swan. That trip could take well over an hour. A cab will run somewhere between $10 & $15, including tip.
HTH.