The chances of a "dangerous" encounter are very VERY small. You really have very little to worry about. That doesn't mean that you shouldn't be aware of your surroundings, but very few people/hunters ever see a mtn. lion, let alone have a close encounter with one.

Actually, I'd say bow hunters are more likely to attract a big cat because we use calling more so than rifle hunters do, and the calling will attract predators quicker than any thing else.