I rode across the states in 2004, solo about 75% of the way. I rode the Lewis & Clark from Astoria to Bozeman, then made my own route the rest of the way to New Jersey. By the way, I'm 5'2", small build, and fairly girly looking.
I mostly camped in developed campsites and RV parks, spent a few nights in city/county parks, a few in people's yards/houses/RVs, and a few in motels.
The biggest safety concerns were 0) traffic 1) dogs 2) cities 3) very poor rural areas. I carried mace for "bad dogs and bad men" but never had to use it. Mostly people were super friendly and helpful to me as a solo woman. The few times I had a "bad vibe" about a situation, I just moved on as soon as possible. For example, once I was planning to camp in a city park, but after getting panhandled a couple of times outside the grocery store, I just decided to get a cheap motel room instead. I think if you just keep the radar on, and project an attitude that you are strong and can take care of yourself, not a victim, you will be fine.
I did a few things to protect myself. When people asked me where I was staying that night, I was vague or said I didn't know yet. I didn't ride at night. I didn't free camp much, and when I did, I checked in with the cops. I checked in with camp hosts whenever possible, and asked them to keep an eye on me. When I did free camp, I tried to set up at night, rather than hang around advertising my solo presence for hours before dark. At the same time, I tried to find a place to sleep long before dark, so that if things didn't work out as planned I had time to find something else. If people asked if I was scared, I told them No, I'm carrying Mace. I asked locals about where it was safe to ride and stay.
One of the big lessons of my cross country tour was that people are basically good, especially in small towns. In cities, people are sick of each other, but in small towns, they are friendly and helpful. This does not apply to extremely poor rural areas -- those were some of the scariest places. In those areas, people may percieve a cycle tourist as a rich freak, and want your money.
It's a little different for women, I agree, but I wouldn't let it stop you. The cars and dogs posed a stronger "objective danger" by far than the human threat.
Anyway... feel free to email if you have more questions.....