The best thing to do is get her interested, and then get her her own gun(s) to take to the range with you. That's what I've done with my wife (who like yours had never even seen a real gun other than one in a police officers duty belt) and she's definately hooked. She officially comandeered my Ruger 10/22, our Ruger M77VT .22-250 was bought with the intent of it being her gun because she wanted something that would shoot farther than 50 yards accurately. Now she wants a Browning Buckmark .22LR pistol to learn how to shoot pistols, followed by a Glock 17 9mm when she gets comfortable with the Buckmark. Anymore I hardly ever get to shoot the rifle I saved for months to buy! For every 100 rounds I load up for the 22-250, I get to shoot maybe 5-10 of them, but at least she lets me go the the range as long as she can come too. I guess I can't complain.
She recently authorized my purchase of my Ruger Super Redhawk in .454 Casull for deer hunting next year, and has been bugging me recently about teaching her to load and shoot one of my muzzleloaders so she can go deer hunting too. Unfortunately I think that she's going to have to put off hunting next season, as come the end of December to the beginning of January she'll be 7 1/2 to 8 months pregnant and probably won't be too into stomping around in the woods for 10-12 hours a day. And that's my secret...the only way I get to shoot my guns is if I buy guns that she doesn't want to shoot. She fired my SRH once with a .45 Colt cowboy load and decided she didn't like it, so it officially became MY gun at that point.
I think the sure-fire best bet is to remind her that shooting and range trips are a good way to get out and spend "quality time" together. If you can convince her that you need to get a new gun so you can
spend more time with her, she'll let you get whatever you want and you've got it made!

Good luck,
Mike