My two cents
Get her on a bike ASAP! The thing is....most girls who have coordination, arnt too girly girl and get the opportunity to try out riding love it! I think some of the "problem" is, guys like to "keep" their girl friends clueless to make sandwhiches for them, cheer them on and take care of them. It makes the guys feel macho and loved to have a girl on the sidelines. OR, they dont want them to get into it because if they do, their "buddy" "dude" time on bikes will be less and it will be more of "I wanna go!" "No fair!"
Yep, I get it!
Clue her in
You'll be glad you did. You two can have a lot of fun riding. Ideally some trails in beginning. It's a great fun for couples. Alone and away from the track and all of your buddies if they are obnoxious, so she can focus and enjoy it. And THEN get her on a track if she is interested. Only do this if you think she is a keeper and it is worth it. Otherwise it's not worth the money or hassle. And only if she isnt ridiculously girly girl. Because those types usually are high maintenance, dont make good riders and are not as much fun, except for sex
Opps! Did I say that?
Now, that doesnt mean give up racing or your "dude time" on bikes. Make sure that is understood. Everyone needs their time away from one another doing what they love.