The Colorado Trail Foundation site gives the idea that it is not possible to take public transportation to the trail head. It is possible to take a bus to within .4 miles from the trail head, but it is a commuter bus that does not run on weekends or holidays and it only goes to the plant 3 times in the morning and 3 times in the afternoon.
This is long and boring, but if I wanted a low cost way to fly to the CT and go directly to the trail head, this is how I would do it. Fly into DIA as early as possible on a work day. On the way to baggage pickup stop by the ground transportation desk and pick up Regional Transportation District (RTD) route schedules for AS, 38, 44, 63X and 76. RTD is not the acronym for Rides To Denver - make you wonder what the bus system in Sacramento is called. After you pick up your bags exit on the east side of the terminal through door 511. Board the RTD AS bus where you see all the RTD signs. You will have plenty of time on the bus to study your route schedules. When you arrive at the Stapleton Transfer Center (the airport before DIA was built) catch the either the 38 or 44 westbound. Ask the driver for a transfer and get off at Wadsworth Blvd.
The 38 gives you access to Safeway, Burger King and McDonalds on the transfer. The 44 gives you access to an Ace Hardware and PEP Boys on the NE corner, Walgreens, Red Lobster and a liquor store on the NW corner, Mi Cabana Mexican food (authentic) on the SW corner, and on the SE corner is a Panda King AYCE Buffet, Gemini Restaurant, a bank and a Grocery Warehouse. The Gemini has excellent vegetarian food and the Panda King has an adequate Mongolian BBQ. There is a Post Office south of the Grocery Warehouse.
Next catch the southbound 76 and get off at Crestline, just past Belleview. The suburban REI is at 5375 South Wadsworth.
No rush because the 76 does not start going far enough south to catch the final bus until about 2:30, but you need to arrive at the next transfer before 5:00. The time window is small but adequate.
Get back on the southbound 76 and get off at Ken Caryl Avenue. Walk to the sw corner of Wadsworth and Ken Caryl and catch the westbound 63X. This is the limit of my actual experience. The RTD site shows a transfer off and back on the 63X to get to the RTD stop just before the Lockheed-Martin Visitors. From that stop go downhill to West Waterton and go south. The trail head is .4 miles from that bus stop. Be careful crossing the road. There are about 10,000 people that work at Lockheed-Martin and only one good way in and out. Don’t think those folks are alert drivers just because they are rocket scientists.
Put on your headlamp cause camping is not allowed in the first 6.2 miles of the trail.
food