well buy a flight ticket to Phnom Penh (AirAsia), and take a bus from there to Snooky Ville, easier, less hassle and you will safe a lot of time. Else you take a bus from the BKK airport to Trat, and from there another bus to Snooky, takes you about 12hrs - not worth it. Enjoy your ride.
The bus isn't a bad trip but you might not make it 1 day. As already said, you need to take the bus to Trat , and from there a minibus goes to the border (same bus station). You can walk across into Cambodia, but you'll be hard put to get to Koh Kong (where the Cambodian bus leaves from) for much less than 150 baht on a bike or 250 in a taxi. A bus leaves from Koh Kong about 12 noon for Sihanoukiville (cost last year was 500 Baht).
I spend a night in Trat, which is not a bad place, and then your guest house will be able to sell you a ticket all the way to Sihanoukville with a minbus pick up (so no need to go back to the bus terminal) to take you to the border and then take the noon 'big' bus to Sihanoukville.
Despite the fact that the trip from the border to the bus in Koh Kong is supposed to be included in the ticket cost purchased in Trat - I never managed to get it for free!!
I did this trip in reverse on Friday but I flew from pp to bkk, would recommend this it's an easy way to do it. If you book the flight far enough in advance you can get it for about 1500 baht
Oh and the bus is about 5 hours and costs $5