One possible motive is to rescue someone. Maybe a friend or a family member of theirs has been captured by the Volturi. Another could be to gain knowledge. The Volturi are very old and have a lot of secrets about vampire existence, so they might go there to learn more.
In some fanfictions, they might face a series of challenges. For example, they could be wrongly accused of breaking vampire laws. The Volturi might be very strict and unforgiving in the fanfiction world. Bella and Alice would have to use their wits and powers, if any, to defend themselves. Maybe they would try to negotiate with the Volturi leaders like Aro, Caius and Marcus.
Well, it could be that Bella and Alice are on a mission to learn some secrets from the Volturi. They might be disguised or using their unique abilities to get close to the Volturi leaders. It could also involve some tense moments of almost being discovered and having to use their wits to escape tricky situations.
Perhaps there is a rogue vampire within the Volturi's ranks who doesn't want Bella and Alice there and tries to undermine their purpose. This vampire could be jealous of their relationship or afraid that they will expose some of the Volturi's secrets.
In the Twilight universe where this fanfiction is based, the Volturi kings are Aro, Caius, and Marcus. They are the leaders of the Volturi, an ancient and powerful coven of vampires.
There is also a possibility that a lone vampire, who has a sense of justice or who has been secretly observing Bella and has grown fond of her, decides to take on the Volturi and rescue her. This vampire could have some special abilities or knowledge that gives them an edge against the powerful Volturi.
There could be other vampires that Bella meets during her time as a vampire before the Volturi. For example, some lone vampires who are also trying to stay out of Volturi's radar. They could become her allies or foes depending on their motives.
Power is a common theme. The Volturi are a very powerful coven, and Bella's relationship with them often involves her dealing with their power. Another theme is loyalty. Bella has to decide where her loyalties lie - with the Cullens or with the Volturi. And of course, love. Whether it's her love for Edward or some new relationships she forms within the Volturi world.
Well, it depends on the specific fanfiction. There are countless fanfictions out there, and while the idea of Bella Swan being a Volturi member is not part of the original Twilight canon, some authors like to take creative liberties. In some cases, she might be a reluctant Volturi member, forced into their ranks for some reason. In others, she could be a willing participant, drawn by their power and mystery.
There are many interesting aspects in this kind of fanfiction. Often, it explores a different power dynamic for Bella. She might be seen as a strong and influential figure within the Volturi world, bringing new ideas and changes. Writers may also play with her relationships, like how she interacts with the existing Volturi members in a more dominant role.