One possible interaction is that Bardock could spar with Goku and Gohan. He'd test their limits and see how much they've learned about fighting. Another could be Bardock sharing stories of Planet Vegeta with them, which would be really interesting for Goku and Gohan to hear.
It could change it a great deal. Goku might learn more about his Saiyan roots earlier, which could potentially make him more in tune with his Saiyan side. This could lead to him training differently or having different goals. For example, he might be more interested in exploring his Saiyan heritage and what it means for his power - up potential.
In this fanfiction scenario, it could be an extremely emotional encounter. Goku, who has grown so much in Dragon Ball Super, finally meeting his father Bardock. Maybe Bardock gets to see how his son has not only become a powerful Saiyan but also a protector of Earth. It could lead to some interesting exchanges about Saiyan heritage and the future of the Saiyan race.
One idea could be to focus on Bardock's perspective before his fateful battle. Maybe explore his thoughts about his son Goku being sent to Earth and his own impending doom. He could have some premonitions about Goku's future role in saving the universe.
Sure, there are. One interesting aspect of 'Bardock x Goku fanfiction' could be the exploration of their connection through the Saiyan bloodline. Since Bardock was Goku's father, some fanfictions might delve into how Goku might have been different if he had grown up with his father around. Maybe there could be stories where Bardock survives and trains Goku in the Saiyan ways from a young age, which would be a really cool and different take on the Dragon Ball story.
A frequent theme in 'Bardock x Goku fanfiction' is power. How Bardock's power or knowledge could be transferred to Goku. Also, redemption can be a theme. Maybe Bardock has to make up for past mistakes through helping Goku. And of course, the theme of survival. Stories where Bardock somehow survives and his presence changes Goku's life in the Dragon Ball universe.
In a 'Bardock meets Goku' fanfic, the plot might involve Bardock being brought back to life by the Dragon Balls. He then sets out to find Goku. When they meet, Goku is initially confused but then realizes it's his father. They could then train together and Bardock could teach Goku some long - lost Saiyan techniques. It could also be a more emotional meeting where they talk about Goku's past and his mother.
I'm not sure of a specific highly recommended 'Bardock finds Goku' fanfic off the top of my head. But generally, fanfics with a high number of reviews and positive ratings are likely to be good. So when you search on FanFiction.net or AO3, sort the results by the number of reviews or ratings. Check out the ones that seem popular and read the summaries to see if they match what you're looking for in terms of Bardock finding Goku.
A fanfiction might explore the idea of Bardock seeing Goku's life through a time - space rift. He witnesses all of Goku's battles and the friends he makes. Bardock is filled with pride but also realizes that Goku has a different path than the traditional Saiyan way. This makes him question the Saiyan culture he once knew. Meanwhile, Goku starts to have strange dreams about his father, which leads him to search for more about his Saiyan heritage.