I recall private taxi services commonly advertised on the street in Hua Hin. Hua Hin to Phuket would likely be relatively expensive. Suggest you take the first class train to Surat Thani - the hop off point for Koh Samui - ideally with a partner (cabins are for two). Book early if possible, in BKK or before arrival.

You can take the bus from Surat Thani to Phuket. Phantip Travel run from the station or their office in town. A little rustic but better than the backpacker ripoff operations in this part of the country.

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