a couple years ago I was in CO - and there were a couple of fellows who were bike/camping from Frisco to Salida - they had first put a vehicle in Salida. They were biking the Colorado Trail - and at segments where the trail is wilderness (and off limits to bikes) they took logging roads and etc. They were weaving down into a town (ie Buena Vista for breakfast and repairs) then back out. I was hiking various segments and ran into them several times - once almost literally.

If you are starting in Denver, my recommendation would be to start at the foothills just west of Denver off I70 for day or two. Hundred of miles of trails around Golden and the hogbacks. After you hit some front range trails, head west on I-70, you could hit Breck, Vail, or even Eagle. Eagle has great mountain biking. Spend two three days in the mountains, then head to Fruita, which is more desert and tons of singletrack. Avoid Moab.

Your best option for better camping and a little more remote would be to go out 285 from Denver, hit some front range trails south west of Denver (Kenosha Pass and CO trail) then head out 285 to Buena Vista area, then Monarch (Monarch Crest) and Selida area. Probably better camping options and less people going out 285 to highway 50. Your last stop should be the Gunnison area.

What Summit says. Crested Butte is a mountain biking mecca, and it's an hour north of Gunnison. Consider rerouting your trip and starting in the Gunnison area, hit Monarch Pass, Gunnison, and CB. Simply amazing.

Crested Butte is your spot. Consider flying to Grand Junction - closer than Denver and you can ride Fruita nearby GJ on your way to CB (though the drive from Denver to CB is beautiful).
The riding in CB is world class and you will not be able to get to all of the trails here and at Hartman Rocks in Gunnison. Several bike shops and I don't have a real recommendation - there'll all fine as far as I know. I'm not a camper so can't speak to that, though there are many places to pitch a tent.

Great mountain bike scene in CB, great town/restaurants.

Go to App Store and download CBGtrails app - it will show you all the trails in the Gunnison Valley

We are actually 30 minutes north of Gunnison. That is unless you drive 30 mph on hwy 135. If you are flying into Denver the suggestion to head up 285 is a good one. If you are looking to rent hit Salida first and shuttle the Monarch Crest or do some trails in the area. Lots of fun rides and for a rental just hit a local bike shop. I don't know the shops down there but the people are good people. Wherever you go they will steer you right. There is camping in the Salida area, plenty of it. Just ask the folks at the bike shop. When done in the Salida area, return your bike, head over Monarch Pass and turn right at Gunnison onto 135 and head up to Crested Butte. You can rent at Big Als or head up to CB Sports on the mountain. Both are solid bike shops who can also help you pick out the best trails for your skill level. There is a lot of camping around the area, not much in the way of facilities but you can do dispersed or hit a forest service campground. Take a shower at the hostel if you want to clean up.

Late summer early fall is a great time to come visit. The weather is perfect and the crowds of tourists from the south and the Front Range have finally left.

Fly in to Grand Junction and rent your bike from Over the Edge Sports in Fruita.
You must ride the Kokopelli Trail. YouTube Horse thief Bench. That is an extreme, but the riding on the mesa as well as the other trails are amazing.
Also check out Lunch Loops and Book Cliff.
Moab is about 2 hours away. I believe Crested Butte is also around 2 or so hours away.
If you go to Crested Butte, check out a trail called 401, also known as 40Fun.
If going in late August, prepare for chilly nights but great Temps during the day.

Thanks to everyone for your replies. It looks like I'll focus my research on the Crested Butte, Gunnison, Monarch area. Can't wait to get out there.