Key to the issue as some have cited is acknowledgement of the hazards in the environment and willingness to equip and train with available/selected tools to overcome the hazard.
If the woman wants to live in a beautiful but hazardous environment:
1. and does not want to train with a heavy caliber firearm, then select a lesser desirable caliber that she will train for (AR platforms, .38's/357's, 9mmm etc.. Classic example would be the small calibers popular with the ladies in cities from the 1880' to 1930's. These are not optimum, but if they fit the constraints of the Lady, better than nothing.
2. and does not want to train with firearms, then Bear Spray is an option. In my opinion it is a much lesser option for reasons others have cited plus more. Once again a better option than nothing, but she needs to train to use it. The Bear Spray industry does very well at $30 to $50 per canister - with strong advocacy/requirement by our Environmentally Centrist (Tree Huggers) Park Service, Forest Service, etc...
3. Many packers, campers, etc.. have Bear Spray and assume in a crisis they can use it. If they have not trained with it, in all probability they will freeze up and not use the Bear Spray, or be ineffective in it's use. To translate the same human reaction to a City Condition, a variety of organizations (Red Cross for one ,as I just heard one of their ads on radio) advocate for training family members for reaction to fire alarms and fires and have recurring family drills on how to respond to a fire. In a fire one normally would have a minute to several minutes to react. In the case of a Bear Attack it's going to be a couple of seconds based on most reports (by the survivors, not the arm chair critiques over the non-survivors). Practice and drills result in a reaction based on "Muscle Memory/Habit", not a thoughtful deliberate reaction.
Key to the answer is acknowledgment and acceptance of the environment, selecting a tool/s to address the danger within the constraints, and having the training/practice necessary to use the tool/s should the need arise.
Personally I prefer to carry either my Kimber or Springfield 1911 when out and about in the Woods and feel confident with them should an animal attack (4 or 2 footed); yet I mostly carry a Beretta 32 Tomcat when in the Town/City - not because it's the best caliber for dealing with a problem (2 footed?) , rather because it's small enough to always fit into a jeans/shirt/coat pocket and I have a tool with me all the time, not back in the vehicle or house. I leave the Tomcat at the house when I leave "Civilization" because I have and am willing to use better tools for the environment.