I'm sure there are. The Twilight saga has a huge fan base, and fanfiction writers love to play with different scenarios. Bella's character is central to the story, and her relationship with vampirism is a key aspect. A story where she turns into a vampire as a result of suicide could be a way to explore deeper emotions, different character arcs, and new relationships within the Twilight universe. However, such a topic can also be quite dark and might be treated with different levels of sensitivity in different fanfictions.
To adapt to her new vampire life in the fanfiction, Bella has a long journey. At the beginning, she struggles with her speed. She might accidentally run too fast and crash into things. But with Alice's guidance, she learns to control it. Her vision also changes, and she has to learn how to focus in different lighting conditions. Socially, she has to interact with other vampires. Some might be friendly, like those in Alice's coven, but others could be hostile. She has to learn how to defend herself and navigate the complex vampire politics. She also has to come to terms with the fact that she'll live forever now, which means leaving behind her human concept of time and mortality.
The Volturi could be antagonists. They are the powerful vampire coven that enforces vampire laws. Since Bella's transformation might not follow the normal protocol, they could see her as a threat to their order. They might come after her to either destroy her or bring her under their control.
One interesting plot could be Bella's struggle to control her new vampire instincts. For example, she might have a hard time dealing with her sudden urge for blood while trying to maintain her relationships with her human friends and family. Another plot could be her discovery of new vampire powers that are unique to her. Maybe she can do something no other vampire can, like communicate with animals on a deeper level.
One common theme could be redemption. Maybe Bella's suicide is seen as a moment of great despair, and her transformation into a vampire gives her a chance to make up for it or find a new purpose. Another theme might be power. As a vampire, she gains new abilities and has to learn to control them, which can be a major part of the story.
Often, other vampire clans that oppose Bella's transformation can be the main antagonists. They might see her as a threat to the vampire world order. For example, a traditionalist clan that believes humans should not be turned so easily could try to harm Bella or drive her away from Edward.
Well, one consequence could be that she has to distance herself from her human friends. Since she's now a vampire, she might be afraid of accidentally harming them. For example, her scent might be too alluring to them, and she could lose control. Also, her family relationships would change. Her father, for instance, would be left in the dark about her true nature, and she'd have to keep lying to him, which would create a strain on their relationship.
In some fanfictions, James might justify it by saying he sees great potential in Bella as a vampire. He could claim that her beauty and tenacity would be enhanced, and that she would have eternal life to experience the world in a way she never could as a human. Also, he might say that she was already on the fringes of the vampire world because of her relationship with Edward, so becoming a vampire was just the next step.
For Edward, it could be a huge shock and a source of internal conflict. He might struggle with his feelings for Bella as a vampire, different from the human Bella he fell in love with. The Cullen family might be divided in their opinions. Some might be worried about Bella's ability to control her new vampire instincts, while others might be more accepting.
In many such fanfictions, a key plot point could be the internal struggle Carlisle faces. He is a moral vampire, so turning Bella goes against his principles at first. He might worry about how Bella will adapt to the vampire life, with its bloodlust and the need to hide from humans. Another plot point could be Bella's reaction. She may be initially excited at the prospect of immortality and being with Edward forever, but then realizes the sacrifices she has to make, like leaving her human family behind.