From the airports:
During the winter tourist season, from December to Easter, the transfer service Fly Ski Shuttle connects the Verona (Valerio Catullo), Bergamo (Orio al Serio), Milan (Linate), Treviso (Antonio Canova) and Venezia (Marco Polo) airports to Val di Fassa.
Info & booking: http://www.flyskishuttle.com
From the railway stations:
FiemmeFassaExpress offers direct connections from airports and train stations to Val di Fassa by private transfer.
Info & booking: http://www.fiemmefassaexpress.com