There is a bus operating between Suvarnabhumi airport and Hua Hin. The bus can stop in Cha-am, just mention it when you buy your ticket at the airport, at Hua Hin bus station or by Internet (you can buy tickets beforehand, it is actually recommended).
At the airport you will find the bus at level 1, gate 8. Departures at 07:30, 09:00, 10:30, 12:00, 13:30, 15:00, 16:30, 18:00 and 19:30.
In Hua Hin the bus departs from the bus station near soi 96/1. The first bus leaves at 06:00, then 07:30, 09:00, 10:30, 12:00, 13:30, 15:00, 16:30 and 18:00.
Travel time is approximately three hours, and the price is 269 baht/person.
Phone number: 084-697-3773 (Hua Hin) and 02-747-4448 (Bangkok).
Here are some pictures of the bus, a comfortable 22-seater.