Bangkok -> Kuala Lumpur -> Singapore: need ideas?

I was reading my Bangkok Travel Guide and I looked at a map and I noticed that Kuala Lumpur is not far away from Koh Samui which is where I plan to vacation. I also noticed that Singapore is not far from Kuala Lumpur. I'll have 2 1/2 weeks total vacation time. What do you think about doing this? I plan to travel by bus or train since I don't have much money (probably by bus). Does anyone have advice? According to my travel book when you get across the border to Malaysia, you have to be kind of wary when you get back on the bus after clearing customs because it might not be the same bus.