I'd go with this approach. Let her know you enjoy the sport of shooting. Phrase it carefully, but ask if she's ever shot a gun, and offer to take her on a safe, controlled trip to the range to let her experience it, so she'll be able to understand firearms better. Be very neutral in how you phrase everything. If she flat out refuses, buh-bye. If she accepts, take her, do minimal safety training so you don't overwhelm her, just enough so she can get up to the line and shoot a couple times. Then gauge her reaction after she's done. That will help guide you in the future there grasshopper.