Ultimately the question is what's going to resolve the situation in the best way to ensure you can work well together in future, and I don't honestly think this is going to do that, @Chunkychipschops.
As another pp has said, this kind of complaint is hard to evidence- you didn't catch her with her fingers in the till. You say "she crossed a line", but that's an opinion; others might disagree and unless you have witnesses, the senior manager isn't likely to accept it as an objective truth. Remember he's also closer to her than he is to you (he's her line manager, not the office behaviour ombudsman).
More to the point, you've chosen to try and put responsibility for policing the relationship into someone else's hands instead of managing it yourself, which isn't generally the approach senior managers want to encourage or reward. You've come back to post in a way that seems quite defensive, so I don't know how far you're open to disagreement, but I do think you'd be hard pressed to find any HR professional who would have advised this as the right course of action. He will now be wondering not only whether you are a poor performer, but also whether you are able to handle conflict in working relationships, as we all have to from time to time.
I don't know if you're familiar with the Parent-Adult-Child dynamic from psychology- I'm no expert on it, but it sounds as though she communicated with you in a "parent" state, and you responded in a way that accepted your "child" role instead of reframing it as an adult-to-adult interaction. The "adult" response would have been to communicate calmly and clearly that you were finding the interaction difficult, that you'd like to find a way to explore how you can respond constructively to her feedback, but that you suggest finding time to do so another day. This gives you back some power in the exchange, instead of trying to hand all the power to an outside authority.
There are a lot of resources to help you manage difficult workplace interactions in future- I find Miss Claire Benjamin on Instagram useful, for example, and there are many others. But I think you do have to start by reframing your ideas about what your own responsibilities in the workplace are, and perhaps taking a less passive approach in future.