>>202326I did that this summer, OP. The motorcycle trip through RMNP, that is. I went from Utah to Missouri and back again, meeting up with family along the way. I found it difficult to camp while traveling by bike, though, to be honest. You get to the campsite, and set up your tent before dark because riding in the dark is dangerous, but you basically have no privacy in a campground without a car; no way to secure your gear when you go hiking; and have limited options for storing food safely away from bears at night. Most campgrounds also close up shop in the mid-evening, so if you don't get there early enough to check in, and if they don't have an after-hours fee deposit box, you'll have to camp "illicitly" until they come by in the morning to collect. There's no sleeping in your car with a motorcycle.
I ended up staying in hotels/motels almost every night of my trip. Next summer, though, when I do this again, I'll bring a book to read in camp and just pack minimally so even if something were stolen off my bike, I wouldn't miss it. Definitely a great trip, but I did not do much hiking overall. I just couldn't stomach the thought of leaving my fully packed bike at the trailhead all day, or even overnight.
>>202361As far as experience goes, I did my bike trip with approximately 7 months of total riding experience under my belt. It was the first time I'd even ridden a motorcycle more than 100 miles at a time. /o/ can help you shop for bikes and gear, but I settled on a Suzuki Boulevard C50. If I did it again, I think I might have gotten a Kawasaki Vulcan instead, but I ended up with a fine bike with low mileage for just about $3000. You'll want something with 750cc minimum displacement for extended highway riding. Cruiser-style bikes are more comfortable for long hauls than sport bikes. Another option I seriously considered is the Honda Shadow 750, although they aren't fuel-injected so they might be more finicky to start in cold weather.