I have never heard it put that well from a man or a woman. It's not that we don't appreciate input from men, but it can be a bit insulting to have someone telling you there's no danger just because he hasn't experienced the danger. It's no skin off your nose to just acknowledge that some people face trouble that you don't, just because of something arbitrary like sex or race or orientation, and that it's not easy to fix.

Back to the topic: I take the same precautions on my bike that I do as a pedestrian -- stay in well-lit areas and preferably well-populated ones, and be aware of where people are so that I can see if anyone's approaching me (which I hope everyone's doing on a bike anyways!). In a park I could probably make a point of riding more than a hockey-stick's-length away from thick shrubbery that I can't see into.

I don't carry any kind of weapon. I suspect that pulling out a gun or a can of pepper spray would waste a lot of time that I could be using to get away, at least when I'm on a bike. I have taken martial arts lessons and I think I'd feel more confident with my hands free than fumbling with a weapon, but that's just me.