Well, maybe Vegeta would be shocked to see Future Bulma at first. He might be confused about how she got there and what the future holds for them. Then they could start to share stories about what has happened in their respective timelines.
Maybe in the fanfiction, Future Bulma meets a younger Vegeta who has been sent to the future by some time - related accident. At first, Vegeta is confused and angry, but Bulma's intelligence and determination start to intrigue him. They could have a series of adventures together, with Bulma trying to help Vegeta adapt to the future while also using his strength to protect what's left of their world.
Vegeta could become more empathetic. Meeting Future Bulma might expose him to different perspectives and make him understand the consequences of his actions better.
Their relationship might start off rocky. Vegeta is a proud Saiyan and Future Bulma is a strong - willed woman. But as they face common enemies and challenges in the future world, they begin to respect each other. Vegeta might start to see Bulma not just as a weak human, but as a valuable ally. And Bulma would see the growth in Vegeta and start to develop deeper feelings for him.
Perhaps Vegeta Jr could challenge Vegeta to a sparring match. Vegeta, being the proud warrior he is, would accept. During the fight, Vegeta Jr might display some new techniques he's developed, which could both surprise and intrigue Vegeta. And in the end, they could form a stronger bond as they realize they share the same values and goals as Saiyans.
Since we should avoid the 'lemon' aspect which is often not appropriate, in general Vegeta is usually depicted as a strong and proud character. He might be shown as a mentor - like figure to Pan in fanfiction. Pan, on the other hand, is often a curious and energetic character. In non - inappropriate fanfictions, their relationship could be one of mutual respect and growth, with Pan looking up to Vegeta for his power and experience.
If Minato survived, it might lead to a power balance shift in the ninja world. His presence could prevent some of the later conflicts or handle them differently. Also, his relationship with his family and friends would evolve in interesting directions.
A possible plot twist could be that Vegeta Jr is actually an imposter sent to deceive Vegeta. He could initially seem like a legitimate Saiyan but gradually reveal his true motives, which might be related to an enemy's plan to take down Vegeta.