Take her out. I was dating my girlfriend for about 6 months or so when I took her out for the 1st time. But make sure you have everything planned nicely. Scout it out, make sure the weather is nice, and the chance of success is good. The more enjoyable you can make it the better.
I took my girlfriend out for the 1st time deerhunting and she shot this buck. Now she's hooked. I have it on video, and it's easy to see how excited she was. I'll take her out for a turkey here in a couple weeks, and hopefully I can get her her 1st turkey also.