This is the way to go. You will pay between six and twenty five Bath for a bottle depending on the size, brand and location. If you're planning a long stay you might want to buy the twenty liter bottle. Since the Thais don't drink the tap water themselves you can be sure that the water you're served at restaurants is from a bottle and not from the tap. If you buy a salad it might have been washed in tap water though so it's a good idea to ask about it.
Ice is also pretty safe in Thailand.
It's made from processed water. This goes for all places, from the luxurious hotels to the street side vendors. A big bag of ice will cost you five Bath.