Well, having been in a situation where I damaged both my parents' car and someone else's: first of all, show some understanding. You just damaged someone's car, people can be very proud of their cars. Tell her you're sorry if you haven't already. Don't think of her reaction as 'overreaction'. She probably just wants her car back the way it was and if she's never had car damage before, she won't know what's needed to get her car back to its original state.
Don't go telling her 'oh, that's a minor thing, we can just polish this away'. A 15 cm long, 0.5 cm wide 'scratch' might very well look worse than it is to someone that's proud of their car. Instead, tell her you will do everything you can to make this right. Feel free to suggest polishing if you have experience with repairing car damage.
If you're not an expert in repairing cars, she won't take your word for it. She'll just think you're trying to handle this as cheaply as possible, and that the cheap solution might be forever visible on her precious car.
Don't go telling her that you're only willing to pay for the polishing away... because that doesn't sound like you want to do everything you can.
- its just a minor scratch and both of us are not looking to using our insurance here
- the repair cost won't be worth the paperwork and time spent on dealing with it.. It is a really petty scratch but yet she's going so overboard
I nicked this from the comments. As said above, tell her that you will do everything you can to make this right.
At the same time, you don't have money to help her have the full bumper paint job she wants/might need. So, state the facts.
It's best that you get the insurance company involved here, whether you want it or not. YOU can't pay for the repairs she might need, at the same time, she doesn't think the scratch is minor and doesn't want to try the cheap solution first.
Get the insurance involved, have them assess the damage and pay for the repairs. So contact them right now. If you wait until the receipt comes in, they might well decline it because it's for more than was necessary.
Right now you're saying that YOU think the damage is minor, and not worth the time/effort. Will it have been worth the time/effort once she decides that the cheap solution wasn't enough, that she still can see a little spot, and decides to get who-knows-who involved to get her right, the full paint job she wants?
The insurance company certainly isn't going to pay for expensive repairs if things can be solved cheaply.
The insurance company has experts that can decide whether this is really minor or needs more expensive repairs.
You are insured so that when such things happen, you don't have to pay for expensive repairs out of your own pocket.
If the insurance company decides she isn't getting the expensive repair but the cheap one, she'll have to fight the insurance company if this isn't enough, not you.
Seriously, if you want to show you'll do anything you can do to make things right, don't go refusing to get the insurance company involved. Get the time and the paperwork and just do it. You damaged someone's property, it's up to you to make it right.