Hi Halifaxmum. I've been reading your story and the replies you have had with interest. I have never been in either your, or your mum's situation but I am able to look at it from an outsider's point of view.
You said in your last message, "you don't care". And yet you obviously do or you would not have taken this step in the first place.
It may be difficult for you but try and put yourself in your mum's shoes for a moment. She has been living with this action she took all those years ago and, no matter what the reason for letting you go, she, in all likelihood has been regretting it ever since.
Now, out of the blue, she is confronted with the daughter she let go.
She has said she wants to keep in touch and that is a very positive step. She could well have rejected any offers of contact as some in her position do.
The next step is to maybe exchange a few e-mails. Tell her something about your present situation so that she gets to know you a bit better and maybe get more info about hers.
Arrange, eventually, to meet on neutral ground, as suggested, and you may even find her volunteering the information you want without asking.
Patience is the watchword.You cannot hurry this or you may lose her altogether.
I wish you all the best of luck.