i'm an avid biker and a driver, but i can't say who's at fault in this case. first you stated it was a two way road, then you wrote that the biker went wrong way down a one way... did you mean the bike lane?
if she went the wrong way on a bike lane, she MIGHT be legally at fault, though I have to say you still should have looked (and not just rear view mirror) before turning to the right. my sister failed a drivers license exam for precisely that.
I do not know what laws apply where you are - the bike lanes are not as strict as roads...the one way there MAY but MAY NOT mean the same as one way on a regular street - so really can't tell.
She should have been more cautious going down the opposite way on a bike lane. I do that only when I must and then I go super slowly, making sure i'm in nobody's way.
You should have looked.
.... I think you're both in the wrong in a way. Is she seeking any reparations? Or is it just a question out of curiosity?