If I remember, in the movie, while James is tormenting Bella, he stated he had stalked Alice when she was human. However, an elderly vampire turned her and blanked her memory. James then killed the elderly vampire for ruining his hunt.
In the book, Twilight...read the part where James is attacking her. He tellsher how sheis the same person who he was trying to kill when another older vampire was protecting her. She was in a mental institution and that's why she doens't remember her life as a human. The older vampire ws protecting her from him and in order to keep her safe from James, the older vampire turned her in to vampire. James killed the older vampire and not Alice becasue once she was a vampire she no longer appealed to him. That's how she was turned.
it says in the book that when James had Bella in the ballet studio, he was talking about the only person who had gotten away from him. he goes to say that he tried to hunt the girl in the mental institution she was located at. right before he could get to her though, one vampire that was working there decided to save her by changing her into a vampire. then James concluded by killing the worker.