I've done a few solo centuries and rarely stop besides the usual breaks. Just in case I use a small cable lock.
Usually, I can pack enough gels, energy bars, bananas, and such to fuel me for the entire ride. A restroom is more important.

Plus, I feel perfectly safe. It's not like Colorado is the wild wild west.

Organized rides are nice, easy, and fun due to the support and comradery but a solo century is perfectly doable and fun in its own right.