Maybe there are some new characters introduced in the fanfiction as well. They could be other vampires or even humans who get caught up in the drama of Edward's attraction to Bella's blood. For example, a new vampire who smells Bella's blood and decides to target her, or a human who accidentally discovers what's going on and becomes a part of the story.
There could also be other characters from the Twilight series like the Cullen family. They might play important roles in trying to help Edward control his urges or in protecting Bella from any potential threats that come with Edward's struggle. For instance, Carlisle, being the more level - headed and experienced vampire, could try to give Edward advice on how to deal with this situation.
Well, obviously Edward and Bella are the main characters. Edward, the vampire, is central to the concept as he is the one with the struggle regarding Bella's blood. Bella, on the other hand, is the object of his dangerous attraction.