I went to Florida in June with a friend of mine and her daughter who is 14. Her daughter was deathly terrified of riding even the kiddy coasters. We hit all of the major parks in Florida over that week and during the first part of the week we gave her major grief about not riding, but we were there to have a good time too, so she just had to wait. Finally, we just took the approach and said that it was ok if she just didn't want to ride, and let it be.
On the last day we were there, at IOA, we convinced her to ride the Flying Unicorn and she had a good time. She rode it several times, but was still reluctant to consider anything bigger, so we let it be.
About a half hour before the park closed, on our last day there no less, we got in line for our last ride on the Hulk, and as we pulled into the station, there stood her daughter in line! We were shocked to say the least, and she looked terrified. I didn't know how she was going to react so I asked my friend, and she said she would either get off crying or dying to go again. Needless to say, she got off with a huge smile on her face and had to run around for one last ride!
It was amazing to see someone experience their first "real" coaster and enjoy it. We even extended our vacation one day so we could go back on Saturday and let her ride some more, including Dueling Dragons. No question that the jump from the Flying Unicorn to the Hulk and DD was a huge one, but if a 14 year old girl can do it, anyone can!
I think your best bet is to get her to go with you , but just lay low, don't pressure her to go on the rides with you, just let her see how much fun everyone who is getting off had and see where that goes. One other thing we did was to get her to wait in line with us, making sure that she knew all she had to do was walk right through the train and not ride. That helped her get over her "fear of the unknown" as she was able to see how the loading process worked and the everyone came back to the station in one piece lol
Good luck in your attempt, as I don't know anyone that didn't love coasters after they got that first ride. I assume she has ridden some smaller woodies from the way that you wrote your question, so you already have a good start as we couldn't even get her on the kiddy coasters.