Agree that women should put some stress through their joints and bones but I don't know if running for fitness is a good solution. I mean, running is GREAT for fitness but the impact can certainly take it's toll. If you can run pain free and you enjoy it, that's great. However, if impact is an issue for you, an alternative has to be found. In this case, women should still do something to offset the osteoporosis IMHO, such as strength training. I think strength training is better than running for that purpose anyway. Running won't strengthen your arms/shoulders much.
Well, running
is a good solution for the reasons you mentioned: excellent for fitness, and very effective at improving bone health. It's unequivocal that it's an especially good tool for both of those purposes in general. I sincerely doubt more than 10 - 15 miles weekly is needed to do the trick, and that's a volume that won't bother most people who run with good form, posture, and who aren't obese.
Now, as a further point, I understand that running seems to bother your own joints more than that. I think you're in the minority for men your size and fitness level. As I say, impact is a hormetic, and thus it is possible to overdo it for anyone. You won't see me arguing that a large volume of impact isn't bad, but where the line is will be well beyond what is beneficial for the bone health of most otherwise healthy women.
Whether strength training is
better for the same purpose is a different question entirely. For the bones and joints that are most at risk for injury from osteoporosis (legs, hips, low back) I would say that impact is superior to resistance training. I'd also recommend both anyway. IIRC, resistance training improves bone health mostly (only?) near the tendon attachments, and, as such, isn't sufficient all by itself. But I don't know for certain. I also don't know how effective running is at improving upper body bone health (if at all, although I suspect it is). However, that region of the body is at a much lower risk of injury from bone disorders, and, as I say, I'd recommend strength training regardless.