I was a minority in the UK for twenty years. I would say two things to that.
(1) It’s a mistake to assume that someone of the same ethnicity is automatically your friend because they feel familiar, any more than they would be if you met them in your country of origin.
(2) They may not want to befriend you just because you share a background.
I tended to avoid people from my country when I moved to the UK, if anything. If I’d only wanted to hang around with people from there, I’d have stayed at home! That didn’t mean I was unfriendly, I simply didn’t think we needed to automatically become close friends, just as I didn’t need to befriend the parents of children my child liked — I would have that child over, absolutely, and the accompanying parent if the child was young, but unless I genuinely liked the parent, I didn’t befriend them.
This woman may feel similarly. If, as you say, you struggle socially, she may not want you to latch onto her. It’s not her job to make it easier for you in groups.
Anyway, it doesn’t particularly matter why. She’s made her position clear. She doesn’t mind an occasional chat, but doesn’t want to befriend you.
I absolutely get that rejection hurts, but it’s happened to us all at one time or other. I don’t struggle at all socially, and there have been times I’ve made overtures of friendship and it’s been a no. You just say ‘Oh, well’ and move on.