Yes, there are some. You can check out fanfiction platforms like Archive of Our Own. There might be various interpretations of this crossover, some focusing on their battles, others on how they could form an unlikely alliance.
The Devil could be the main antagonist. Since he is Cuphead's main enemy in his own game, he might follow Cuphead into Bendy's world. He could see Bendy's world as a new place to spread his evil and also wants to get revenge on Cuphead. He could start causing chaos in Bendy's world, which would force Cuphead and Bendy to team up against him.
One possible plot could be that Cuphead and Bendy accidentally cross paths in a strange, in - between dimension. Cuphead, being his adventurous self, is intrigued by Bendy's spooky appearance. They initially have a bit of a stand - off as they don't understand each other's motives. But then they realize they both have a common enemy, some sort of dark force that is threatening both their worlds. So they team up, with Cuphead using his shooting skills and Bendy using his ability to disappear into the shadows to fight this new threat.
A corrupted version of one of their own friends could be the main antagonist. For example, a possessed Boris from Bendy's world or a mind - controlled Mugman from Cuphead's world. This would add an emotional layer as they have to fight someone they care about.
Perhaps Bendy and Cuphead are forced into a competition by a mysterious villain. They start off as rivals but gradually realize that they need to work together to defeat this common foe. This could involve them using their unique abilities, Bendy's flexibility and Cuphead's shooting skills, in creative ways.
A common theme is the clash of their different art styles. Cuphead has that rubber - hose, 1930s - style animation while Bendy is more of a creepy, old - timey cartoon look. Another theme is adventure. They often go on quests together in fanfictions.
One common theme is friendship. Since Bendy and Cuphead are from different franchises, a lot of fanfiction focuses on how they become friends. For example, they might start off as rivals but then realize they have more in common than they thought.
I'm not sure of a specific one off the top of my head, but you can start by looking on popular fanfiction websites. Search for 'Cuphead Hurts Bendy' and sort through the results. Look for ones with high ratings and positive reviews from other readers.
One common theme is the struggle between good and evil. Since Cuphead as a vampire might have some dark tendencies, and Bendy could be on either side of the moral spectrum in different fictions. So, their relationship often explores how they deal with their own natures.