Thanks to Robert Pattinson Source we have a first description of new 'New Moon' scene shown at the Rome Film Festival today.
Edward leaves Bella:
Edward is waiting for Bella at her house, because they need to talk. He tells her he needs to leave Forks because Carlisle is raising suspicions in town.
At first Bella is convinced that Edward wants to take her with him, but then starts realizing that's not the case.
She asks Edward: “What do you mean by “us”?”. He responds: “Only my family.”
Bella gets upset. Tells Edward again that the incident with Jasper was nothing, and Edward answers that is exactly the problem: “Nothing compared to what could have happened.”
He tells her she doesn't belong in his world. Bella answers “Well, that changes many things.”
That is when Edward says line we've seen in the trailer “This is the last time you'll see me.”
Bella tries to convince him to stay, that she's not afraid to lose her soul, but Edward doesn't give in.
The scene ends with Edward leaving. Screen then goes to black and we see Bella fall to the ground.