I would suggest NOT making her first flight (or anyone's) a cross country. First-time fliers are often nervous - You know how the public's perception of safety is altered by the media - And those nerves, combined with every little bump, may make someone airsick or at least nauseous. Having a "mission" to accomplish will lead them to not say anything to you for fear of messing up the mission.
With that in mind, you should take her flying just to go flying, at least once before you start with the missions. My trick is to ask MSN approach for a "city tour." I take off, we fly past the capitol, Camp Randall Stadium and the rest of the university, over their house if they're from the area, and then I go back and land before they even have a chance to think about being nervous. It's a positive experience for them, and they not only look forward to the next flight, they're a lot less nervous the next time.
Be *very* careful what you say, too. I know that you study a lot of the risks involved in flying and the shortcomings of some aircraft. This is not good dinner conversation for the night before the flight.
Even talking about why it's safe can be detrimental. For example, I took my best friend and his daughter flying. He's a nervous flyer. He started telling her that "There might be a few bumps in the air after takeoff, but it's not dangerous at all." She probably never would have even thought about danger until he said that.
Anyway, once you get her in the air for a quick (1/2 hour) flight, then start with the short cross country flights. You also said she's never been in a plane before - Even an airliner? Wow. If that's the case, you may find that she likes it enough to take it up herself, or at least enough that she lets you do more aviation-related trips in the future.