FWIW - i had a girlfriend in college that was really pissed at me when i bought a handgun. She had not interest in shooting. I did not push it. I would go shoot (1-2x) and then she was around when I cleaned it. Just before she was sure that the relationship was over, I asked her to pick up the parts while the gun was in pieces. She picked up the parts and quickly started asking how it worked. Slide off frame and barrel in slide she began to see the mechanism. Another time or two she commented that the gun was merely a tool and realized that if the operator pulled the trigger it would fire, and if not then it would not just fire by itself. THE LESSON - EDUCATION. SHe learned not to be scared because she understood the mechanism. This is not different that learning to drive or doing anything for the first time - take it slow and easy, don't push or she will resist.
The following weekend, we went to the range, found a quite place with just hte the two of us. I did not want others around as she would be nervous and ditracted. I wanted her to focus on what we were doing. She shot the gun and promptly went though 200+ rounds with a perma grin on her face. To this day, she does not hunt and does not want. SHe is ok with hunting as she understands where meat comes from. (Once met a woman in the grocery store that shought meat come from the store, she had no idea it was from a cow and was equally appauled and crying when she learned that lactating cows produce milk - uneducated)
Moral of the story - education is everything, but some people wil learn and not like what they learn, while others will ike it. Needless to say, I married the college girlfriend and over twenty years later she still pushed me out of the way to get to the firing line first.
Whether your girl will shoot or not is not the issue. If she is willing to learn and respect your choices that it was matters. Don't push her to do it. And for god sake if she does don't be an ass and get her behind a 12 gauge or a hand cannon. Seriously go with the 22lr if you can. Also, use a handgun that fits her so the recoil travels into her wrist and forearm correctly and does not bend her wrist to the side. Remember, her first ecperience will dictate the learning curve and if it hurts or is painful, she will continue or develop a negative image. My wife started with the 22lr pistol and now she shoots a 12 gauge and 44 mag. Oh, she is 120 lbs and 5'4" too.
Good luck, let us know how she does.