Edward would still be a very important character. Since he's Bella's love interest in the original 'Twilight' series, in the fanfiction, he would play a major role in Bella's new vampire life. He might help her adjust to her new powers and the vampire lifestyle.
One interesting plot twist could be that Bella, as a new vampire, discovers she has unique powers that no other vampires have. For example, she might be able to control the elements in some way.
One interesting aspect could be how their relationship dynamics change. In the original, Edward was the vampire and Bella was the human, so reversing their roles might lead to a different power dynamic. For example, Bella as a vampire would have more physical strength and speed, which could make her more protective of Edward. Also, Edward as a human might struggle with his mortality compared to Bella's immortality, creating new tensions and storylines in the fanfiction.
One great fanfiction could be where Edward and Bella's relationship is explored more deeply in a different vampire society setting. For example, they might be in a vampire clan that has unique rules about human - vampire relationships.
In such a fanfiction, it could change the entire dynamic of Bella's relationship with the other characters. Maybe she'd be more confident and powerful from the start.
One popular 'Bella is already a vampire' Twilight fanfiction is 'The New Life of Bella Swan'. It takes the concept and explores how Bella's relationships change when she's already a vampire from the start. Another is 'Bella's Vampire Beginnings' which delves into her early days as a vampire, her new powers and how she copes with the vampire lifestyle.
One common theme is the exploration of Bella's transformation into a vampire in more depth. Another is the relationship between Bella and Edward, but often with a new twist. For example, some fanfictions might focus on how they deal with different challenges as vampires together.
A common theme is the 'what - ifs'. What if Bella had chosen Jacob instead? Fanfictions often explore this alternative storyline and how it would affect the vampire - human relations in Forks. It can be really interesting to see how the characters develop in this different scenario.
Perhaps some of the other Cullen family members would be her allies. They are already vampires and could help her adjust to her new powers and the vampire lifestyle. For instance, Alice might use her power of seeing the future to guide Bella in making important decisions. Jasper could teach her how to control her new vampire instincts, like the urge to hunt. And Emmett could be her sparring partner to help her improve her combat skills.
Jacob could also be a common character. Even though Bella has become a vampire, her past connection with Jacob and the werewolf pack might still play a role. There could be some tension or new interactions between the vampires and the werewolves. And of course, Carlisle, as the head of the Cullen family, is likely to be in many of these stories to guide Bella in her new vampire life.