Buses to Hua Hin from Bangkok’s Southern Bus Terminal on Pinklao - Nakhon Chaisi Road (in Thonburi); 232km, 3-4 hours
non-aircon 42 Baht, 5:00 - 19:00 every 30min;
aircon 74 Baht, 5:00 - 22:00, every hour,
2nd cl 65 Baht, 6:00 - 19:00 every 30min.

From the Westin to the Southern Bus Terminal, easiest would be to take a cab....traffic in the morning won't be bad between 9.30-11.30am

There is no airport bus to between the airport and the Southern Bus Terminal, but local Bus no. 10 goes to the Southern Bus Terminal from just outside the airport, so there must be a similar bus service in the opposite direction.