Join Date: Jun 2011
Location: Lock Haven, Pennsylvania
Year/Make/Model: 2001 Kawasaki Vulcan 1500L Nomad FI
A passenger backrest would not automatically solve it, no. She needs to be comfortable using it in order for it to have any benefit. When I was getting used to riding two up, my shifts weren't that good and I'd get a thunk whenver up- or downshifting, nevermind a hard braking situation.
The both of you getting used to the new scoot will help with this problem. Yes, it's annoying, but tell her to relax and that she won't slide off (be sure to guarantee this, it'd be awkward turtles all over if she did). If it doesn't get better, a backrest might be the best option, but again, she'd need to be comfortable being that far back.
I'm sure you'll find a solution, and once you do, the REAL fun can begin.