Once again, Bella is the first woman in the movie. The film opens with her narration as she runs through a crowd of people. At about the two-minute mark, Bella's grandmother is seen, although she doesn't speak-- and it turns out, it's actually Bella, in a mirror, in a dream. Edward has one line in the dream.
Charlie, Bella's father, wakes her up and says, "Happy Birthday" at the three-minute mark. Following Edward's line in the dream, Charlie is the second man in the movie.
The second woman in the movie with lines is Bella's friend Jessica, who reminds Bella of the Romeo & Juliet essay. Mike is the first to call Bella over to the group, and responds with his own lines right after the exchange between Bella and Jessica, so it could be debated whether Bella and Jessica are talking to each other, or talking as part of the group (which includes both Eric and Mike).
Regardless, once Edward and Bella go into the school, Alice approaches them and gives Bella a present. They exchange a few lines, and Alice invites Bella to the Cullens' house that night. Edward is present, but doesn't say a word, and Jasper is looking on, but at a distance. New Moon passes all three levels of the Original Bechdel within the first ten minutes.
In class, everyone is watching a film of Romeo & Juliet, while Edward and Bella quietly talk to each other. The male teacher, Mr. Berty, stops the movie, and says, "Now, who'd like to repeat the last few lines of iambic pentameter just to show they were paying attention? Mr. Cullen?" Edward replies, "Yes, Mr. Berty," and recites several lines from memory. Unlike the first movie, New Moon quickly passes both the Original Bechdel and Reverse Bechdel.
If there's any doubt about the in-class conversation between Edward and Mr. Berty, New Moon passes RB-2 again when Bella is lost in the woods. Charlie and some other men are standing outside, talking about trying to find her. One of the men says the Cullens have left town, and Charlie asks where they've gone. Another man says "good riddance" to them. There are no women present in the scene until Sam carries Bella back, so it clearly passes RB-2. It may also pass RB-3 since they talk about the Cullens, although since they only talk about the Cullens within the context of how to find Bella, this may not pass RB-3.
However, at the movie theater, Eric and Jacob talk about the movie Face Punch, including how Eric doesn't really like action movies, and Jacob isn't old enough to buy his own ticket. He mentions Bella (she's buying his ticket for him) but the conversation up to that point takes place between the two