One reason could be to create a more independent storyline for Bulma. By having her avoid Vegeta, it allows the writer to focus on Bulma's own growth, her friendships with other characters, and her scientific achievements without the influence of her relationship with Vegeta. Also, it could be a way to introduce new and interesting plot twists. For example, how Vegeta would react to being avoided and what steps he might take to try and win her back or at least find out why she's avoiding him.
In a 'bulma avoiding vegeta fanfic', there are many directions it could take. For example, Bulma might receive a warning from a psychic about staying away from Vegeta for her own safety. So she decides to take a sabbatical and go live in a secret underground base she had built long ago. She could also be so engrossed in a new project, like building a super - advanced spaceship, that she simply has no time or inclination to interact with Vegeta. Another idea is that Bulma accidentally stumbles upon a portal to a magical world and decides to stay there to avoid Vegeta.
Maybe Bulma is too busy with her scientific research and family matters to be interested in fanfic about Vegeta. She has a lot on her plate, from taking care of Trunks to working on new inventions.
Maybe in the fanfic, Vegeta did something unforgivable like betraying Bulma's trust or putting her in great danger while under the influence of the Majin transformation. For example, if he endangered their family or made a pact with the enemy that directly opposed Bulma's values.
Vegeta would likely still be his proud and strong - willed self, but with a newfound tenderness towards Bulma. He might be a bit more protective and less quick to anger. Bulma, on the other hand, would be her intelligent and sassy self, always ready to challenge Vegeta in a playful way.
One day, Vegeta was training as usual. Bulma, with her fiery spirit, walked up to him. 'You know, Vegeta, you can't just focus on fighting all the time.' Vegeta scoffed but deep down he was intrigued. As time passed, he found himself looking forward to her visits during his training. Their relationship grew slowly from her constant nagging and his reluctant acceptance to a deep love. They learned to understand each other's quirks and became an unlikely but powerful couple in the DBZ world.
No, it is not appropriate. Writing such fanfiction involving sexual content about fictional characters is disrespectful to the original work and its intended audience. Fanfiction should focus on positive aspects such as character development, new adventures, or alternative storylines within the boundaries of good taste.
Their relationship would likely become more intimate and committed. With a baby on the way, Vegeta would probably be more protective of Bulma. He might show his love in more practical ways, like making sure she has everything she needs.
At first, they might be at odds. Vegeta could be seen as cold and aloof, while Bulma is more outgoing. Bulma might try to befriend Vegeta, but he brushes her off. However, as time goes on, he starts to respect her intelligence when she helps him with a difficult class assignment.
It could be that they have a very different interpretation of Naruto's character. However, this is a very extreme and negative way of expressing that view. They might not understand or appreciate the values and growth that Naruto represents in the original story, and instead choose to write something so unkind.
One reason could be to explore alternative scenarios. They might think 'what if Naruto had this super - broken power?' and write a fanfic around it. Also, it could be a way to stand out. In a sea of Naruto fanfics, having a really out - there concept like a 'broken' Naruto might attract more readers.