What is the best way to get from the Hotel Amadeus hotel the Seville airport?
Best needs defining, but I'd take a taxi: https://www.aena.es/en/sevilla/getting-there/taxi.html
For the bus, enter "aeropuerto" in the search bar at https://reddelineas.tussam.es/?lang=en
We were just in Seville and our hotel booked an early morning taxi to the airport. It took less that 20 minutes and cost 8 Euros.