I am a single female who has camped alone for much of my 30 years. I primarily stay in campgrounds, but many are remote, and I've frequently been the only one there. (Did freak myself out one night when I was the only one in the campground and we had a wicked windstorm and I was deep into a Dean Koontz novel...). I've never had a problem. It may help that I frequently have a few large dogs with me...
As I've gotten older and had some health issues, I'm slightly less adventurous, but still camp lots on my own. If I have cell phone reception (not always), I'm never really alone... 😎
Start with where you're comfortable and go from there, and keep your eyes and ears open. If you feel uncomfortable, don't stay.