What about the Bustang bus to Vail?

Bustang's West Line runs Denver Union Station to the Vail Transportation Center for around $15 to $21 and it is genuinely good value. Two things to plan around: it leaves from Union Station rather than the airport, so you need the A Line train in first, and it drops at the transportation center rather than your lodging, so you need a local bus or taxi at the other end with your luggage. Budget three to four hours door to door. If you are travelling light and not in a hurry it is the cheapest realistic option.