We all have friends that we would just LOVE to get to ride bikes with us. But sadly, you can lead a horse to water but you can't make them drink, as they say.
Your friend sounds like the kind of overly cautious person who even if you could get her to buy a bike, probably wouldn't ride it more than a couple of times. The first scare she has and back to the garage the bike will go I bet.
We just can't always get people to behave the way we'd like, or to do the things we know are good for them.
I predict that even if you did convince your friend to get a bike and ride with you, she would likely only want to ride a mile or two at a speed so slow it would drive you insane.
My advice?- just appreciate your friend for how she is without trying to change her.... and look to find a riding buddy among people you encounter who are already cycling.