I've done it a lot traveling in general, and was planning on doing it on a bike this summer until a buddy jumped at a halfway joking offer that I never figured he'd take. I can say in general, for my personality, I prefer solo travel. But, that is me.

Just use common sense. Are you riding along roads where if you have an issue, there'll be a car by in a few minutes, or in the middle of the wilderness where you may not see another person for days? There is a big difference in how safe an average person would find each for a solo traveler.