Do bicyclist have the right away to randomly dart across oncoming traffic?

So I’m driving down a road at approximately 40MPH. Suddenly, a woman riding her bike on the right-hand shoulder of the road comes darting through my lane as to cross to the other side of the road. Note that there was no Stop sign, crossing/pedestrian crossing, or traffic light anywhere remotely close to where she decided to do this at. If I had not have slammed on my breaks and swerved – I would have hit her. I then fully extended my arm and applied the palm of my hand firmly against my horn for a good 10 seconds as she crossed. Then she has the nerve to scream out “F YOU!”, as if I had done something wrong.

Did I do something wrong? I honked my horn not because I was angry – but to let her know she could have ended her life and possibly endangered mine and any other possible surrounding drivers by what she had done.