Without a car, the FASTEST way to get to the Boardwalk is to take the bus to MGM and then the boat to the Boardwalk area.
If the boat stops at the Swan/Dolphin first, get out there and walk over to the Boardwalk. Otherwise you will then have to wait for the boat to load, continue to the Yacht/Beach Club, unload and load and then over to the Boardwalk.
However, the first stop coming from MGM may be the Boardwalk.
This is the reason we ALWAYS rent a car.