Best way to go in Koh Samui from Bangkok

There are several ways you can do the trip. Bus/ferry, train/bus/ferry or fly.
Here is a complete breakdown of timetables and costs using various means of travel.
Enjoy your trip.

Thanks mate, I really appreciate. Have a good day

hello,

I also recommend the Lomprayah ferries to visit Koh Samui or the other islands (Koh Tao, Koh Phangan) from there.
lomprayah.com

As you have only a few days in Bangkok I would look at flying down to either Surat Thani with Thai Lion Air and getting the ferry over to Samui for about 2,700 THB return or if you aren't worried about the cost you can fly direct with Bangkok Air to Samui for about 13,000 THB return.

Good luck with your travels.

Air Asia will fly to Surat Thani with bus/boat connection and Nok Air will fly to both Surat Thani and Nakhon Si Thammarat with a bus/boat connection to Samui

I usually take the bus and ferry combo at FerrySamui. It's the site that I use whenever I travel from BKK to Koh Samui, Phuket and Phangan. They are pretty reliable. Their prices are very cheap too which is perfect for me as I'm a budget traveler. Hope this is still useful. Cheers.