It is in book 2, "New Dawn," that Edward decides that he and Bella should not see each other. The Cullen family throw a party to celebrate Bella's 18th birthday, and as she often does, Bella has an accident. This time, the accident almost costs her her life, and Edward decides it is just too dangerous for a human and a vampire to try to have a romantic relationship. During their time apart, Bella grows attached to Jacob Black and learns more about the world of the supernatural.

I don't want to give too much away, but the story does have a happy ending.