In this fanfiction scenario, Goku could meet Bulma when she was a child. He could befriend her in a different way compared to their first meeting in the original story. Also, he could run into King Kai at an earlier time and start training with him much sooner, which would significantly boost his power levels and change the course of his battles in the future.
Well, he could change a lot of things. Maybe he'd prevent some bad events from happening in the past. For example, he could stop Frieza from destroying Planet Vegeta earlier. It would be really cool to see how his super saiyan power affects the past timeline.
Well, perhaps Goku travels back in time to meet his long - dead parents. He could have conversations with them, learn about his family's history in a more personal way, and gain new insights that help him in his present - day battles. Or he might go back to the time when the Saiyans were still on their home planet, and try to change the fate of the Saiyan race by warning them about their impending doom.
Well, he might change some crucial events. For example, he could prevent some villains from ever rising to power. Maybe he'd stop Frieza from destroying Planet Vegeta earlier, which would change the whole Saiyan history and his own life. He could also teach his past self some new techniques, making the Saiyans even stronger in that timeline.
In such a fanfiction, Goku might be seen as a very powerful and strange visitor in Konoha. He could start by showing off his amazing strength and speed during a training session with the ninja. Maybe he'd accidentally break some training equipment and leave everyone in awe.
If Goku travels back in time as a Super Saiyan in fanfiction, his relationship with his past self would be complex. His past self might look up to him as a hero and a mentor, but at the same time, there could be some envy or confusion. With his Saiyan comrades, he could become a leader figure much earlier, changing the power dynamics among them. Also, his interactions with Earthlings would be different. They would be more fearful or more in need of his protection, depending on how he uses his power in the past.
Goku might run into past versions of his friends. He could see a younger Krillin or Bulma and have some really interesting interactions. He could also meet past versions of his enemies and try to change their fates. For instance, he could meet a young Vegeta and try to steer him away from the path of evil. This would be a huge change in the Saiyan's story.
It could be Iruka. Since Iruka is an important teacher in Konoha, he might be the first to notice Goku's arrival. He'd probably be cautious at first, not knowing what to make of this powerful being, but then try to figure out if Goku is a threat or not.
She could meet the founders of Hogwarts. Imagine Hermione having a conversation with Rowena Ravenclaw about the importance of knowledge and wisdom. She might also meet Godric Gryffindor and learn about the true meaning of courage from him. Another person she could meet is Salazar Slytherin. It would be very interesting to see how she would interact with him, given his views on blood purity.
She could experience the historical events of 1918 first - hand. It was a time of great change. There were things like the end of World War I and the start of the Spanish Flu pandemic. Bella would be in the middle of all that chaos or transformation.