While I'm sure that you are well meaning, and this comes from a place of love for your daughter, I hope you haven't approached your daughter to discourage her from this trip.
As a solo bike tourist (who also happens to be a women) I can tell you a couple things:
1) As another poster said, your 25 year old daughter is likely much more versed in the dangers of womenhood than you are likely to know. She is making a decision based on her knowledge and you should respect that.
2) Despite the constant barrage of news stories related to violent crimes, the U.S. (indeed the world at large) is a much SAFER place than it was 40 years ago. You enjoyed your own adventure then; support your daughter in her choice to do so now.
3) Most people are generally kind to randoneers and touring cyclists. The general response is curiosity and wonderment, not animosity or ill-intent.
4) Here is my general protocall to make sure things go smoothly on long distance solo trips:
Have a fairly solid itinerary. Share your plan with those close to you, so they know where to expect you, when. Keep in contact with at least one person to let them know about your progress. Be well versed in camping/sleeping options along your route. Be flexible when you need to.
Don't tell random non-cyclists that you meet where you're camping. Don't excessively highlight that you're solo (although I've never hidden this info either). Oh course, feel free to talk to people in the community, as this is an enjoyable part of touring.
Secure your stuff while camping. I am a frequent hammock user, so that means keeping my stuff underneath me and my bike nearby. Use your common sense while camping. If a campground seems busy or excessively exposed, keep your belonings closer. If a campground (or camper) makes you feel uncomfortable, leave. I have definitely pulled into some sketchy camp areas along the coastal route from Seattle to San Francisco and decided I'd be better off to put in another 10 miles than sleep somewhere that seemed risky.
5) Please don't act like women are frail creatures that cannot complete ambitious tours. This idea has been rooted in male minds throughout the history of the bicycle and women keep proving you wrong. Unless there is something that you are not sharing about your daughter (a medical condition or a need for supervision in her daily life), please stop acting like your adult daughter cannot accomplish this reasonable goal.
Last edited by angelabikes; 08-22-19 at 09:08 AM.