Coworker trash talking about me

"Dave? He can piss off, i dont want to speak to him". The issue is she knew I heard but didnt even apologise.

That's bad.

You don't want people to not speak to you. You need to identify why this person doesn't like you, and stop doing what ever was the cause for their discontent with you.

You've probably done something to inadvertently offend her, without realising it. The best thing to do is to have a chat in private. Ask her if you've ever done something to offend her, because if you have you really want to apologise. If she says everything is fine, then say "strange, I heard you say *blah blah* about me. I'm just really worried I've upset you. Are you sure there is nothing I can do better?"

Won't help. She's nice to his face, and talks about him behind his back. She will just say, "Oh no, it was something silly. I thought you'd done something" etc.

OP just stop helping her.

How does not helping her help OP in any way. The only thing that could do is undermine his already damaged relationship with a colleague and bring him into disrepute around the firm as somebody who is unhelpful - which will mean he won't get promotions, bonuses, or help from others.

People are always nice to your face when they need you for something. What do you expect?

At the very least, she will brush it aside as nothing. But she will feel quite superseded by OP because OP knew what she said about him (making him appear omnipotent - she'll be less inclined to undermine him the future because of this) and OP will come from the moral high ground saying he wants to build bridges with her, which will likely make her feel guilty because OP has shown he is attentive to her opinions.

Unrelenting niceness is far more powerful than childish petulance.