The aircon buses and VIP buses are run by the government Transport Co., by ChokeananTour and Suwannatee Tour. They all depart at the Southern Bus Terminal in Bangkok and most of them go to Chumphon bus terminal on the highway from where you have to take a songthaeo to go to the city center or to one of the piers.
The private aircon buses from Chokeanan Tour end at the aircon bus terminal in the city center next to the market. From there it is easier to get a songthaeo to the pier.
A third private company is said to be more efficient. We are still checking this out.