Generally, you are safe alone. You must understand this country is riddled with crime and there are no guarantees. The fact is anything can happen at any time. Being alone on a bike with all those drivers passing you puts you in eyesight of a great many more people than would see you in a car. In a car only those going faster than you get a look. On a bike just about everybody passes you. A loaded touring bike attracts attention at stops and on the boulevard. There are psychopaths, drunks, crack heads, inexperienced drivers, and the impaired elderly out there cruising around. Weeks ago a cyclist was stabbed to death at McDonalds in Vero Beach, Florida by a mentally ill homeless man. There was no reason whatsoever for the attack. Cycling cross country means many stops at C-stores, restaurants and other places for food and drink. You are generally safe. Be vigilant. Trust your senses and hunches. If he looks suspicious or sinister, he probably is. Beware of anyone who will not give you a last name or proof of it. Be very vigilant at any truck stop. Serial murderers working as long haul truckers have abducted and killed many women. Most if not almost every one of the women were prostitutes. There is a website about this by the FBI. You should be safe. Do not throw caution to the wind. Be careful and aware.