On occasion with prior cars, I also used to use a california duster. However, with the Maserati (mine is also black), I noticed that I was beginning to induce some marring. My Maserati is a total dust magnet.
As for washing the cover, it is about removing any dust or anything else that may have settled on it. It's inevitable that anything that had settled on the cover will end up on the inside of the cover while taking the cover off and storing it.
2012 GranTurismo Sport Cabrio Black/Black
2009 Aston Martin DBS, 6 speed manual, lightning silver/black