I rode my 2000 VFR800 out that way.
There's a thread about it:
To Beartooth and Back
I did
Pikes Peak which was gorgeous, and a must. My bike has a primitive Fuel Injection system and it was fine. The only difference I noted was louder cracks and bangs from my exhaust on decel, but I like that sorta thing.
I also rode west from Pikes Peak to Leadville, Colorado and from there I rode
Independence Pass towards Aspen. Independence Pass was amazing too. Highly recommended.
Regarding elevation changes, some roads will have steeper and tighter curves than others. It shouldn't be a problem of any rider that isn't completely green. Just take it at your own pace.
When I was going up Pikes Peak I ended up behind a group of riders on big cruisers and touring bikes. At one point the last rider in line panicked in the middle of a hairpin and just stopped. Luckily I was able to go around but it could have been worse.
(see 08:40 for the turn in question)
As Lightcycle said, your body will be more effected by the altitude than the bike. I felt off when I was there. Just meh. Drinking tons of water helps.
At the top of Pike Peak which is over 14,000ft I felt a bit dizzy.
If you have any questions don't hesitate.