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.
Perhaps they suspect that the Volturi are involved in some dark plot. So, Bella and Alice decide to go there to investigate. They might also go to the Volturi to prove their innocence if they are wrongly accused of something. And in some fanfictions, they could go there just out of pure curiosity to see what the Volturi are really like.
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.
Perhaps she is deceived. In some fanfictions, she could be tricked into believing that the Volturi are the 'good guys' or that they can offer her something that the Cullens can't. It could be a false promise of safety or a way to protect her loved ones that leads her to become a Volturi member.
One possible motive could be jealousy. If Mike has feelings for Bella and she is interested in someone else, like Edward in the Twilight series, he might be driven by envy to attack her.
One possible plot development could be that the Cullens launch a rescue mission. They might gather other vampire clans to help them, as the Volturi are very powerful. Another could be that Bella discovers some long - hidden secrets about the Volturi while in captivity, which changes her view of the vampire world completely.
One consequence could be that Bella becomes more isolated. Without Alice's acceptance, she might not have access to the support network that Alice provides within the vampire community. This could make her more vulnerable to enemies or just generally more alone in that new world she's entering.
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.
Perhaps in the fanfiction, Bella has been influenced by a darker force. It could be a new vampire or some other supernatural entity that has turned her into a bully. This external influence could be warping her mind and making her act out against those she once cared about or new people in Forks.
It could be revenge. If the human had wronged Bella in some way, like harming her family or friends in the fanfiction world, she might be driven to kill out of a sense of vengeance. Or perhaps she is forced into a situation where killing seems like the only option to protect a greater good, like saving a whole community from a dangerous human.