We met this nice Dutch girl in Chile who was traveling South America alone for six months. Her she is in Peru. Her parents were worried sick about her she says. We met a couple of weeks before she was to return to Holland and she didn't want her adventure to end. She is 24.
Before I met her I would have told you don't do it. But since meeting her and two other women, as your father I would say, "bad people are a rare exception in this world. Go for it"
A bike trip in the US is a chance you may not again have a chance to do. Take advantage and get on your bike and go.