St. Augustine Airport does not have any scheduled commuter flights to anywhere,. All flights are charters. Airport Express of St. Augustine runs an ground transport to Orlando International(MCO) and Jacksonville International(JAX). They do door to door service 24/7. 904-824-9400
There is a shuttle from Orlando to Daytona, but I don't know of one that goes to St. Augustine. But there's a good possibility you could hire it to go further. There are a couple of companies that I know of. The primary one is DOTS. Daytona Orlando Transportation Service. I've only seen the other buses a couple of times, so I'm not sure of the name.