For a collision causing damage or injury in the UK, by law you must:-
"-give the following to anyone with ‘reasonable grounds for requiring them’, for example an insurance company:
your name and address
the vehicle registration number
You also need to give the owner’s name and address if the vehicle is not yours.
You must report the accident to the police within 24 hours if you do not give your details at the time of the accident.
You must also report the accident to your insurance company, even if you’re not planning to make a claim. "
It is quite common for people to try to circumvent the legal requirements by offering to pay for damage directly, I would imagine that this woman has been shocked by the cost of repair and is hoping , because you are
a foreigner, you will just "Go away!"
I would say you have two ways to proceed,
1. Ask your insurance company to find the woman's insurance details and claim for the repair against it. That's what you pay them for, after all.
If that is not possible, then make a claim in the 'Scottish small claims court' against her. This can be done online and the 'simple procedure can be used for any amount under £5000.
Here is a link to the claim form
Simple procedure