Yes, there are some out there. You can try looking on fanfic websites like Archive of Our Own or FanFiction.net. Just search for 'beerus x bulma' and you'll likely find a variety of stories with different takes on their relationship.
The contrast between their characters. Beerus is a powerful god of destruction, while Bulma is a brilliant human scientist. Their different natures can create really interesting dynamics in a fanfic.
Their relationship could be developed through shared interests. For example, both are interested in unique and delicious food. Bulma could cook special dishes for Beerus, which would gradually make Beerus see her as more than just an ordinary Earthling. He might start to respect and even protect her in return.
Maybe there's a plot where Beerus has a premonition about a threat to the universe that only Bulma's technology can help prevent. So, he has to team up with her. Along the way, they learn more about each other's worlds. Bulma gets to understand the power and responsibilities of a god like Beerus, and Beerus discovers the amazing potential of Earthling technology. This could lead to a deeper friendship or mutual respect between them.
One idea could be that Beerus is intrigued by Bulma's intelligence and her ability to create amazing inventions. He might start visiting her more often, causing some comical misunderstandings among the Z - fighters. For example, Vegeta could get jealous of their interactions.
One possible scenario in a 'Lord Beerus in love' fanfiction could be that he falls for a mortal. This would create a huge contrast as he is a god. His love for the mortal might make him question the differences between gods and mortals. He might try to find a way to make the mortal immortal so they can be together forever. It could also cause conflict among the other gods who might not approve of such a relationship. They could see it as a disruption to the natural order. And Beerus would have to fight against their opposition to be with the one he loves.
There could be. Fanfiction is a creative space where all kinds of wild ideas are explored. However, this particular concept seems rather unorthodox considering Gohan's relationship with Bulma in the original Dragon Ball series. Gohan has always seen Bulma more as an aunt - like figure. But in the world of fanfiction, anything is possible. It might be difficult to find though, as it may not be a popular or widely - accepted concept.
There may be such fanfics in the vast world of fan - created content, but it often goes against the original storyline's intended relationships in the Dragon Ball series. In the official story, Goku is married to Chi - Chi, not Bulma.