Af far as Trail Ridge being open you couldn't count on it but it might be open, From the national park service in 2012:
Trail Ridge Road historically opens on Memorial Day weekend; last year, due to historic snow accumulation, the road opened on June 6. This year's opening is the third earliest day that Trail Ridge Road has opened since the road was completed in 1932. The earliest day was May 7, 2002. In 1963, the road opened on May 11. Trail Ridge Road is the highest continuous paved road in the United States, climbing to 12,183 feet and connecting the towns of Estes Park and Grand Lake.
and from a local paper in 2013:
Trail Ridge Road historically opens on Memorial Day weekend; last year the road opened early on May 14. The earliest the road has opened was on May 7, 2002; the latest June 26, 1943.
You can browse ACA routes here, I doubt you will go through Steamboat Springs.http://tsteven4.qwestoffice.net/maps/GreatParksRoute.html
It is possible to ride up the I70 corridor to Idaho Springs, then you can pick up the Great Parks South. Willow Creek Pass on 125 is nice. It is very unlikely that you wouldn't be able to ride Idaho Springs, Berthod Pass on US 40 Granby, Willow Creek Pass on 125 and on to Wyoming in May, these roads are open year round except during avalanche control or heavy snow storms. Lookout Mountain, from Golden, would be a good way to start up, this is how we started the Western Express from Boulder. You cannot ride on US 6. I live in Boulder and ridden most of these roads multiple times. I would still do Trail Ridge if it was open, and the above route if it wasn't. If you do Trail Ridge I could suggest routes to get there, we had historic flooding last year and some of the canyons are still a mess.
Colorado cycling maps are available here:http://www.coloradodot.info/programs/bikeped/colorado-bicycling-maps/scenicbywaysbikemap.pdf/at_download/file
They will mail you a paper copy,
For a hard copy of Colorado State Map, send your name and mailing address to firstname.lastname@example.org.
As far as getting across Denver I would be tempted to get on a bus! In general the RTD has bikes racks, although at the airport they might put your bikes underneath, if so you wouldn't want to unbox them before the bus. I imagine you could ride from DIA, but in 30 years of riding in the area I have never headed in that direction, it seems so much better to head up and west into the glory of the Rockies. I used to look unfavorably on this sort of thing, but a few Russian cycling clubs in Moscow taught me that it can be best, they always take the train out of town.http://www.rtd-denver.com/Bike_n_Ride.shtml