It should be noted that there are no buses traveling across the island, going from one side of the island to the other.
Every bus goes to the main bus station at Fira (the capital of the island) and any changeovers for the next bus destination must be made from the main station only. The journey from the airport to Fira takes about 20 mins and costs EUR 2.20 each way.
The bus service does not run on a regular basis and may only run every few hours (i.e. 7:30am, 11am, etc), especially in winter. The bus schedule is posted outside the airport and just before the exit.
TIP: It is very handy to have a copy of the bus schedule or write down all the departure times and keep it with you, so you know when the bus will come.