DIA is 3.5-4 hours away from Aspen. However it is a very pretty drive, especially if you choose to go over Independence Pass or Loveland Pass. There are shuttles and rental car options from DIA (including the Roaring Fork Express)
Fly right right into Aspen and take a shuttle to your hotel. This airport offers shuttles, taxis, and car rental services.
Fly into Vail/Eagle county which is only 1.5hr drive to Aspen/Snowmass. Rental car and shuttle options available
This shuttle service offers both private and shared ride options to Aspen/Snowmass from Eagle Vail Airport and Denver International Airport
Book reservations here
Aspen is fairly walkable and also has a great public transportation system (RFTA). RFTA is free within the towns of Aspen and Snowmass. Buses are no more than 15 minutes apart beginning at 6:30 AM-12 AM.
Uber and Lyft are also an option but wait times can be slightly longer than usual