I drove to Phuket 4 weeks ago and only had to show proof of vaccination at the bridge. Not sure about the busses, but I would also like to know.
Cheap, non-stop domestic flights to Phuket are available from Bangkok, Udon Thani, Chiang Mai, Chiang Rai and maybe a few others.
I am driving back down there in the next few days. It is nice to be there with ones own set of wheels. No taxi games to play.