This whole post seems vaguely wrong to me, it smacks of "look at me, look how fit and amazing I am, I can ride 20 miles XC without taking a break"!
It has a condescending tone when you say "
I've told her that if she gets so far and can't ride any more, we'll make our way to the nearest road, I'll ride back and get the car and come and pick her up". You shouldn't even be thinking like this, you should be planning a gentle, five - ten mile or so, cross country jaunt, relaxing and taking in the scenery with your girlfriend and her capabilities totally in mind; it's for her, not for you to show off. If you do it your way a) you're just showing off and

it'll more than likely just put her off for life.
Plan a simple gentle ride. If she laps it up then you can start extending it next time.