Is there shuttle service to the airport?

Yes

As far as remember, the hotel itself does have a shuttle service, although I'm not sure if you can only use it if you park in their lot, or if you can use it either way. They are also right next door (or at least within walking distance) to another airport parking/shuttle service too. We did not use it, so I am unsure how often a shuttle comes. They probably call a shuttle for their guests rather than having it on a schedule (such as Superpark and the like who come every 10 minutes or so), due to more than likely not having as much "shuttle required" business as the airport parking lots whose main job is to take people to and from their lots. I hope I've helped at least a little!