Well is there anything for her to lean her back against. There is nothing worse then being on the back of a bike with the feeling that you might slide back words. Get her a backrest and I guarantee she will not hold onto you, and you will forget that she is back there.
Don't believe me, hop on the back of someone bike and let them drive you around. It can be scary.
Because the two of you are "beginner" 2Up riding I suggest take it very easy with her and make sure that she understands how the bike accelerates, brakes, and turns and don't hit anything fast, curvy, etc for a while till she gets used to the bike, and you get used to the bike with a passenger on.
If you scare her now, she will never get back on the bike and you will have lost a riding partner.
What I did with my passenger, took the bike to a empty parking lot as she followed me in my car and plopped a borrowed helmet on her and basically gave her a 30 min class on what to expect with the bike even before we got on it. I made sure that she would lean with the bike, and that if she was going to hold on, to hold on at my waist, how and when to get on and off the bike (when I tell her to, and always from the left side).
Long story short is now every time I grab my helmet, she is ready to go 5 min after that. I kind of miss riding the bike by my self. I still take it easy with her and I pride my self with smooth take offs, turns, and braking. She will let me know if something bothers her (too fast or taking a turn too quickly) and I adjust as needed.
There is nothing wrong with her holding on, just not on the shoulders. My passenger knows that during a hard stop to put both of her hands in the center of my back to keep from falling into me. This way her force is equal on both my arms. This is something we went over when we started out.
By the way.. other then getting on and off the bike, and hard stops, she never holds on me. Get a back rest or a top case with a back cushin. I got a Dan Vessel passenger backrest (Google it) for her and it was the best $125 addition to the bike.. well other then the center stand.
In regards to her sitting back there and not holding on, there is nothing wrong as long as you are not going fast enough to have the wind blow her off.