I feel bad for a girl who sits alone at lunch, but shes said to be annoying and mean?

Just go up to her, smile, say "what's up?" and ask if you can sit down. If she says no, just give her a smile, say thanks anyways, and head over to your normal table. If she says sure, then just sit down and say something neutral. You could make a comment about the cafeteria food, or a teacher in the room, anything non offensive. Just start up a convo. A lot of people use bitchiness as a front to keep distance from people without even realizing it. She might seem a little rude, but as long as she doesn't outright insult you she probably appreciates your effort. If it doesn't work out, don't take it personally. And if your friends give you shiff for hanging with her, tell them why you're doing it. It's always worth a try!