Not sure where in the park you are going to be, but Estes Park is literally the east entrance to the Park. Both US 34 and US 36 run through Estes Park, US 34 is also Trail Ridge Road over the Continental Divide connecting the west and east sides of the park. Most people that are in RMNP are going to be on US 34 at some point, so if you follow US 34 eastbound from anywhere in the park you will arrive in Estes Park. The only hiccup I can see is that this time of year Trail Ridge Road (US 34) is approaching its seasonal closure over the Divide. It is not open in winter, but if you are going to be on the east side of RMNP its not an issue. If you are going to be on the west side of the Divide, please post as the directions to the airport are quite different.
From Estes to DIA: US 36 continues from Estes Park into Boulder, eventually Denver, and meets up with I-70 which you can take east to Pena Blvd and the Denver International Airport. There are "shortcuts" you can take, but if you are unfamiliar with the area, this is probably the easiest as it involves the least number of roads. Just keep an eye on the US 36 signs, as with most US highways its makes some turns.
Thanks for the info guys I should have been more clear. We'll be on the east side of the park, but we won't have a car. So I was more wondering if there is a reliable way to get from a trailhead to the city of Estes Park proper in place of the shuttle service that doesn't run at this time of year.