The OP's route won't work because you cannot take a bus to or from TTC at any resort.
Take the bus to Hollywood Studios. Then either ride the boat or walk to Beach Club.
There are not any buses from Hollywood Studios to Beach Club. There's just the boat. The sequence of boat stops is: DHS, Swan/Dolphin, Yacht/Beach, Boardwalk, Epcot. the boat ride itself will take about 15-20 minutes, not counting time spent waiting for the boat to arrive, empty, load and launch.
I think the only time it is faster to take the boat than it is to walk is if you are going from the Swan/Dolphin to DHS or vice versa, assuming you are not waiting too long for the boat to arrive. Maybe it is easier to take the boat to the Yacht/Beach than walk it, because the BC is the furthest resort in walking distance from DHS. I usually walk it unless the weather is bad.