As long as people tiptoe around her (and encourage you to do so OR advise you to "ignore" her) she will continue.
Again, what do you have to lose? If you leave earlier than planned they'll have no one to train her. So why not say something to her like "You and I will have to work together for the next few weeks so we might as well make the best of it. How about we leave the commentary outside the door and focus on work?" And you could tell your manager that you're not interested in dealing with someone who's trying to be unpleasant, so if they don't want to say something to her you will deal with it in your own way. Assure them you won't be unprofessional but you also won't be treated poorly.
I could maybe understand if you were staying, but you're not. So why not say something?
And ask your fears what it is you're really afraid of. That's how I deal with things that I'm irrationally nervous about.