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 unique element could be the different power dynamics. Since Bella is already a vampire, she doesn't have the same vulnerability as in the original story. For example, her relationship with Edward might not be as protective - based. Another element is how she fits into the vampire society right away. In the normal story, she has to be gradually introduced, but here she's already part of it, so it might change the way other vampires view and interact with her.
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.
Since Bella is already a vampire, her character development could focus more on her coming to terms with her new existence in a different way. She might not have the same initial struggles with bloodlust as she does in the books. Instead, she could be more interested in exploring the vampire culture and history right away. This would lead her to interact with different vampires, not just the Cullens, and gain a broader understanding of their world. This, in turn, would shape her character into a more worldly and independent vampire.
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.
In some fanfics, a possible plot twist is that Bella, as a vampire, has a different sire than Edward. This could lead to a whole new set of alliances and rivalries. Maybe her new sire has a dark past or is part of a vampire clan that is at odds with the Cullens. This would force Bella to re - evaluate her loyalty and her place in the vampire world.
Archive of Our Own (AO3) is also a great place. There are many talented writers who post their 'Bella is already a vampire' fanfictions there. You can search using relevant tags like 'Bella as vampire' or 'Twilight AU with vampire Bella' to narrow down your search.