Goku would probably be really confused. He loves Chi - Chi and their family, and he might not understand why Bulma would want to break them up. He might just tell Bulma straight that he's happy with his life as it is. Chi - Chi, on the other hand, would be furious. She's very protective of her family and her relationship with Goku, and she'd likely give Bulma a piece of her mind.
Goku may initially be a bit oblivious. He might think Bulma is joking or not really understand the seriousness of what she's trying to do. But once he realizes, he'll firmly stand by Chi - Chi. Chi - Chi will go into full - on defensive mode. She'll likely confront Bulma and remind her that she and Goku have a strong bond, and no one can come between them. Chi - Chi may also list all the things she's done for Goku and their family to prove that their relationship is solid.
One possible plot could be that Bulma might be jealous of the relationship Goku and Chi - Chi have. Maybe she sees how much Goku has changed since being with Chi - Chi and she misses the old, carefree Goku. So, she tries to create misunderstandings between them by, for example, making it seem like Goku is more interested in training with her than spending time with Chi - Chi.
Chi - Chi would likely be very hurt at first. But then she would get angry and start thinking of ways to prove to Goku that their relationship is strong. She might cook his favorite meals and remind him of all the good times they've had together, while also giving Bulma a piece of her mind.
One possible motive could be that Bulma is worried about Goku's safety. Since he's constantly getting into dangerous battles, she might think that if he's not tied down to Chi - Chi, he could be more focused on self - preservation. Maybe she feels that Chi - Chi's family demands on Goku are a distraction and could lead to his downfall in a fight.
Goku would likely be extremely excited. He has always had a longing to know more about his Saiyan heritage and his father. Meeting Bardock would be like a dream come true for him. He'd probably ask a million questions about his past and Saiyan culture. Chi - Chi, on the other hand, would be a bit more reserved at first. She'd be polite but also a bit cautious, as she doesn't know what this Saiyan from Goku's past might be like. But as she sees Goku's joy, she'd warm up to Bardock.
Chi - Chi might also be heartbroken. She loves Goku deeply despite his flaws. In fanfiction, she may initially be in denial, thinking that Goku will come back soon. But as time passes, she realizes that he may not return, and this could lead to a deep sense of sadness and loneliness. She has to then figure out how to raise their children on her own.
I'm not sure if there is an actual fanfic with that exact plot. Fanfic topics can vary widely, but this seems like a rather unfaithful and out - of - character concept considering Chi Chi's strong bond with Goku in the original series.
Check out Tumblr as well. There are many Dragon Ball fans on Tumblr who create and share fanfics. You can use the search function to look for Bulma x Goku content. Some Tumblr blogs are specifically dedicated to collecting and reblogging good fanfics. Plus, Tumblr often has fan art associated with the fanfics, which can enhance your overall experience of exploring the Bulma and Goku fanfiction world.
One possible fanfic could be about Bulma and Young Goku's first adventure together. It might start with Bulma recruiting Goku to find the Dragon Balls. They could face various challenges like wild animals and bad guys along the way. Their different personalities, with Bulma being smart and resourceful and Goku being naive but strong, would create interesting interactions.
Love and family are very common themes. Their relationship as husband and wife, and as parents to Gohan and other children is often explored.
You can try fanfiction websites like Archive of Our Own (AO3) or FanFiction.net. These platforms have a vast collection of fanfics, and you're likely to find many Bulma shows Goku fanfic there.