Rebecca, I remember a previous post that a visitor found storage at the bus station, so I called to see if still available, and it is. Lockers are $3 for the first hour and $1 per hour after that. It's difficult to find storage short term because of security/liability, esp. since 9/11. If you are staying at a hotel, they will often keep your luggage for you short term.
There is a luggage storage service a short one minute walk from Union Station in downtown Denver - LUGDEN. You can make a reservation online - lugden.com, call - (303) 747-5600, or show up as a walk-in. They offer hourly, day, overnight and weekly bag storage. Great place to store your luggage if you're on a layover from Denver International Airport, or going to a concert, or headed to a Rockies game at Coors field and want to enjoy yourself without having to lug your bags around.