Have a conversation - talk to her. Chicks dig that
Tell her its important to you. Its something you enjoy, you think she will, and you know you will enjoy it more if it's something you can do together.
You want her to come at least once to get familiar with how the gun(s) operate, and to learn a little gun safety. If she hates it and never wants to come back - you will support that but it would mean a lot to you if she at least tried it. My wife was worried about "being instructed" in public. So we went over safety and function at the house before we ever went out in public. By the time we hit the range the first time, she felt good about loading, grip, stance, etc.
Some folks just don't want to look like they don't know anything in public - maybe that's something holding your wife back too?
The key is - it is something that the 2 of you can do together. Drive that home.
The wife and I often make it a date night. Stress relief/practice at the range and then we hit up a restaurant on the way home. Talk about the session, our day, watch a few innings of the Braves game - whatever.
Pro-tip = having a partner to help clean the guns after is the best part of the whole deal - I'll tell you that for nothing!
Good Luck!