My dd aged 13 was involved in a fall out with another girl at school. They couldn't make up because my dds friends were fuelling the argument either at school or Facebook. My dd was getting upset by it and felt it was getting out of hand. So I called other mum thinking she would be aware but she wasn't. She then went onto Facebook and read some awful comments another girl had written about her dd and is now upset. We got her dd and my dd to talk yesterday away from school and they sorted things out but now I feel bad that this other mum was upset and feel partly responsible.
I think you did the right thing by telling the other mother that her daughter was being bullied. I'm not surprised she is upset. It's good that your dd felt able to tell you about it and ask for your help to sort it out.