Transport from Catania (or catania airport) to Taormina


Hope someone can help me out in here :)

My mum and I are travelling to Sicily this summer. We are arriving to Catania on the 22nd of july at 9.25 and need to go from Catania airport to Taormina. Since it's on a sunday, I am having a hard time figuring out if it is even possible to find any public transportation. I can't seem to find any bus routes, and the only train ride I can find, leaves from Catania centrum at 11.39, which I am not sure leaves us enough time to get to the train station from the airport. Moreover, I can't seem to buy the tickets online, which makes me think that tickets might be sold out when we get there. SO, does anyone know if there's a bus leaving dirrectly from Catania airport to Taormina or at least from Catania city centre on a sundays, and if so, where I can find the tickets? Hope someone can help me, and thankyou! :D