From there it is pretty straightforward to get to the Eastern Bus Terminal or Ekkamai Bus Terminal. Take the BTS towards National Stadium and change at Siam. At Siam take the BTS towards Bearing and exit at Ekkamai. The whole trip from Krung Thon Buri to Ekkamai shouldn't take you more than 30 minutes. Schedule an hour with the taxi from Speak-Easy. The fare for the BTS train was BHT 42. In Ekkamai take exit 2 and the stairs going down to your right. After that, take a left turn at the next possibility, and you will see the bus terminal.
In the bus terminal, go to the ticket teller and buy a ticket to Trat for BHT 265. You will have 2 possibilities, the bus at 22.00 or the bus at 23.30. Either one is good. As I was fairly early, I took the bus at 22.00. It arrived in Trat around 3.30, whereas the other one arrived around 5.00. In any case, you will have plenty of time in Trat to get to the minivan.
In Trat, the minivan service will start between 5.30 and 6.00 in the morning. Before that, just wait or sleep to pass time. People will probably want to sell you a taxi ride to the border for BHT 800, but remember that the minivan will also get you there and for only BHT 120. People will probably also tell you when to get to the end of the bus terminal where the minivan for Hat Lek (border town) leaves. The only constraint is that the minivan might take slightly more than an hour. Mine arrived at the border around 7.10. The bus to Sihanoukville leaves from Koh Kong at 8.00, so you'll have to expedite the border crossing.
At the border you will be guided by locals who will rip you off. There is no way of this not happening to you, even if you speak Khmer. It will be much better if you speak khmer though. In any case, be prepared to pay BHT 1'500 for a business visa (I don't know how much a tourist visa is). The business visa can be renewed in Sihanoukville at a local travel agency. The local helping you expedite the border process will do a really good and fast job (hopefully) and take a huge tip (if you don't give him the proper amount to pay for the visa). On top of that, he still asks for a 100 baht to pay for the stamp.
Then a taxi driver will tell you that the ride to Koh Kong will cost you 400 baht and the bus ticket 600 baht. He will tell you that the bus will most probably be full when you get there. It wasn't full when I got there, but it was low season. Anyway, you will be overcharged, but you can't really negotiate too much, as the driver will just tell you to walk. You can try another driver to see if you can play them down, but that will take you some precious time. The taxi driver will then drive you and your precious visa to the bus terminal in Koh Kong.
The bus ride will take another 4 to 5 hours. At least it will stop shortly at some place where you can eat and drink something. You also get a bottle of water for the ride. In Sihanoukville the bus terminal is way out of town. You will probably find a tuk-tuk that will take you to town for USD 8. It's a good idea to share a tuk-tuk with other travellers. We loaded up our tuk-tuk with four people and all luggage. It looked amazing. I must find that picture!
There you are.