Give this a try:
Arrange a range day with another couple or two. If possible, go with folks she knows and likes. Make plans to go eat lunch or dinner afterwards at some restaurant that your girl loves. Pack a big cooler with her favorite drinks and snacks. Make a big, happy production out of it. Nobody likes to be left sitting at home when everyone else is having fun. She may just cave and want to tag a long.
Make sure to bring an easy shooting .22 rifle. Hopefully, you'll be going to a place where you can shoot up some tin cans or at one of those steel hanging paddle targets made for a .22. The rifle is more important to have along as opposed to a handgun as it's more difficult to hit one's target with a handgun; newbies find it more frustrating. Every newbie I've brought to the range had a ball with the ol' Glenfield 60. They get a satisfied grin on their face when they make that tin can bounce for the first time. And, a .22 rifle has next to no kick or noise so it's not intimidating.
Also, if you can get her to read something for a half hour, the Cornered Cat website mentioned above is very good.
A while back, I was out with a woman who thought I was a bit off for carrying a gun. She wasn't a fanatic about it but she did bring it up a few times, usually when I made the Makarov "clunk" by putting down my coat or when I emptied my pants pockets (P3AT.) Anyway, it was somewhat late and we were on our way home when we stopped at a dingy Minit Mart-type gas station to get gas and a coffee. Some big, loitering drunk started up with us, the what're-you-looking-at type. I told my date to get behind me and to get out the cell phone, that no one was going to hurt her. Thankfully, it didn't get crazy and we got home without incident. But, later, she did very reluctantly admit that she was really glad that I had my gun. I love how folks will be so, so idealistic in the safety and comfort of their living room but will quickly let all of those sacred ideals fly out the window when real life injects itself into their cozy cocoon.
Anyway, try the range outing-picnic-dinner-funtime event. Nobody likes to be left home alone while everyone's out eating, socializing and having fun. My current girlfriend, a very serious relationship girlfriend, had never shot a gun before she met me. I got another couple, both of them CCW folks, to go to the range with us. My girl had a good time, met some new people and now has her own carry permit. She's only carrying a tiny, nickel-plated, 80 year old H&R 5 shot hammerless .32 revolver but at least she always has it with her. It's a babystep, yes, but it's better than a .22 or nothing at all.