Catelyn knows Jon Snow as the bastard son of her husband Ned Stark and some unknown woman. Unlike most bastards of a lord, Jon was living with his father, his father's wife, and his trueborn half-siblings. Ned brought Jon to live with him in Winterfell. This made Jon Snow a living reminder of Ned Stark's infidelity to Catelyn. This was the "one thing [Catelyn] could never forgive Ned."
It was revealed to the audience much later that he isn't what he seemed. R + L = J
Relevant text from the books:
[…] Ned brought his bastard home with him, and called him “son” for all the north to see. When the wars were over at last, and Catelyn rode to Winterfell, Jon and his wet nurse had already taken up residence.
That cut deep. Ned would not speak of the mother, not so much as a word. […]
Whoever Jon’s mother had been, Ned must have loved her fiercely, for nothing Catelyn said would persuade him to send the boy away. It was the one thing she could never forgive him. She had come to love her husband with all her heart, but she had never found it in her to love Jon. She might have overlooked a dozen bastards for Ned’s sake, so long as they were out of sight. Jon was never out of sight, and as he grew, he looked more like Ned than any of the trueborn sons she bore him. Somehow that made it worse. “Jon must go,” she said now.
- A Game of Thrones, Chapter 6, Catelyn II (emphasis mine)
Catelyn never trusted the boy, as I recall, no more than she ever trusted Theon Greyjoy.
- Brynden "Blackfish" Tully (Catelyn's uncle) in A Feast for Crows, Chapter 38, Jaime VI (emphasis mine)
About your clarification:
Just to clarify, I know that she doesn't like him to begin with, but when he enters the room, she is sad, not angry. She only becomes angry after he begins talking to the unconscious Bran and specifically after he invites Bran to The Wall, so it seems like she got triggered by something there.
Catelyn has always disliked Jon and what he represents (to Catelyn). At this point, she is anguished after what happened to Bran. She's not exactly in the mood to hide her contempt for Jon, even in Ned's presence (who was there to witness what happened). Even Ned was not surprised to see her behavior towards Jon. Robb was also aware and asked Jon about it:
Robb: My mother?
Jon (tongue-in-cheek): She was very kind.