In order to get to Phuket you would need to ride 14 hours on air-conditioned buses between Phuket and Bangkok (Cheapest tickets are from Bangkok's Khaosan Road). The easier way would be to go by Thai Airways or AirAsia, which would take only 1 hour and 10 minutes. The flights go out of Bangkok roughly five times a day. There is no rail service to Phuket.