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.
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.
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.
In the original series, they have a rather casual acquaintance. But in fanfiction, their relationship could develop into a friendship based on mutual respect. Bulma could teach Beerus about Earth's technology, and Beerus could share some of his knowledge of the universe with her.
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.
Beerus would likely be more powerful. He is a god of destruction in his own universe with incredible cosmic powers. Naruto is extremely powerful in his world, but his power is mostly based on chakra and ninjutsu, which is on a much smaller scale compared to Beerus' ability to destroy planets with a flick of his finger.
Well, Naruto could be in awe of Beerus' power. Maybe he tries to learn some of Beerus' combat techniques. Since Naruto is known for his determination, he might pester Beerus to train him.