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.
One possible plot could be Bardock's adventures before Goku was born. Maybe it could show how he dealt with the Saiyan politics and his growing concerns about Frieza's rule. This could set the stage for Goku's future battles as his son.
Well, perhaps Bardock would first meet Goku's wife, Chi - Chi. She might be a bit wary of him at first, but as Bardock sees how much Chi - Chi loves Goku and their family, he starts to respect her. Then when he meets Goku's son, Gohan, he could recognize the great potential in him, just like he saw in Goku. Maybe he would even offer some Saiyan - style training tips to Gohan.
In this fanfiction, Bardock might be shocked to see how much Goku has grown and the family he has built. He could be proud of Goku for becoming such a strong and kind - hearted Saiyan. And when he meets Gohan, he might see the potential in him as well, maybe even offer some unique Saiyan training tips that are different from what Goku has taught Gohan.
In this fanfiction, Goku might finally learn more about his Saiyan heritage from his parents. He could have heart - warming family moments with Gine and Bardock that were never possible in the original story.
In a 'Dbz Goku meets Bardock' fanfiction, it could start with Bardock somehow being brought back to life or time - traveling to Goku's era. They might initially have a bit of a clash because of their different upbringings. Goku was raised on Earth with love and kindness, while Bardock grew up in the harsh Saiyan society. But as they get to know each other, they find common ground. Bardock could be in awe of Goku's Super Saiyan transformations and Goku could be eager to learn about his Saiyan roots from his father. They could also form a strong bond and work together to protect the universe from new threats.
One possible plot could be that Goku, having achieved new levels of power, somehow travels back in time to meet Bardock. Bardock, initially shocked, quickly realizes this is his son. They could have a sparring session where Bardock sees the full extent of Goku's power and is proud. Then they might sit and talk about Goku's life on Earth, and Bardock could share some of his own past battles and the reasons he sent Goku away.
For Goku, he could gain a deeper understanding of his heritage. Meeting Bardock would make him more aware of his Saiyan side. He might become more confident in his Saiyan abilities. For Bardock, seeing Goku all grown up and powerful could give him a sense of peace. He could realize that his sacrifice was worth it and be proud of the man his son has become.
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.