Thank you for the info - I also posted a message to the Sevilla info office and got a rather satisfactory reply:
The bus company is called Amarillos Tour, the route costs 2.10 eur and there are a few stops on the way:
Palos de la Frontera (1 parada)
C/ Dr. Pedro de Castro (Hotel Meliá, H. Pasarela)
Enramadilla (RENFE, Viapol)
Avda. S. Francisco Javier (Edificio Sevilla 2)
Avda. Eduardo Dato (H. Hespería)
Avda. Luis de Morales (H. Lebreros)
Avda. Kansas City (Santa Justa y H. Occidental).
From this point on, straight to the airport.
From the airport the bus leaves every 30 minutes - very convenient!
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Palice