Give her a chance, I say. She obviously regrets it - if she's so regretful about it, then she won't do it again. Everyone deserves a second chance.
Don't let one incident cloud your judgement of her. You know her best and you know logically speaking whether she's likely to cheat on your again. Eg, is she normally a reliable person? Are you two normally very honest with each other? If yes, to both, then give her a chance, I think. She told you - she was honest enough for that and she obviously values you and the relationship enough to let you know the truth, so you can come to your own decision about this.
Like, if you dump her now, you'd never know whether you've just dumped a girl you love who would never have cheated on you again. If you gave her a chance and she cheats on you, then at least you know for a fact that she's a cheat, as opposed to just assuming that she is. And if she doesn't cheat on you again, then you haven't just given up on something that could have been mended and gone well.
In the end, it's up to you. You're not wrong to dump her, but it's not wrong to keep her either.