The relationship could start with hatred. Bakugou may initially be enraged that Deku has become a villain. But as time passes, he starts to see the reasons behind Deku's transformation, which could lead to a more complex relationship.
One concept could be that Villain Deku manages to manipulate Bakugou into joining his side. Maybe he plays on Bakugou's insecurities or his desire for power. Another could be a world where they are both villains from the start and they form a power - hungry duo, causing chaos everywhere. A third concept might be that Villain Deku kidnaps Bakugou as part of a grand scheme to get back at the hero society that they both feel has wronged them in some way.
It could start with Deku taunting Bakugou. As a villain, Deku would have a new - found confidence and would use it to get under Bakugou's skin. He might leave cryptic messages for Bakugou, hinting at their past and how Bakugou used to bully him. This would make Bakugou angry but also curious about what Deku has become.
One possible plot reason could be envy. Maybe Todoroki, as a villain in this fanfiction, is envious of Deku's popularity and the support he gets from fans. So, he kidnaps Deku to take away that source of admiration from him. Another reason might be related to power. If Todoroki has turned villain, he could see Deku as a threat to his plans, and by kidnapping him, he aims to neutralize that threat.
Well, AO3 is definitely a great place to start. It has a tagging system that makes it easy to find the specific type of fanfic you're looking for. When you search for 'villain deku x bakugou', you can also filter the results by things like rating, word count, and completion status. Fanfiction.net also has a decent selection. However, you need to be a bit more careful there as the quality control isn't as strict as on AO3. You could also look into Tumblr. There are a lot of My Hero Academia fans on Tumblr who might post about or recommend good villain deku x bakugou fanfics. Some of them might even have their own fanfic blogs where they share their work.
A possible plot is a power struggle between them. Since Deku has turned villain, he might see Bakugou as a threat to his plans. Bakugou, on the other hand, wants to bring Deku back to the light. This creates a constant back - and - forth of battles, both physical and psychological, as they try to outwit each other.
Midoriya's friends like Uraraka and Iida would be extremely worried. They would immediately start looking for him. Uraraka might use her quirk to search in the air, while Iida would lead the ground search with his speed. Bakugo, on the other hand, would be furious. He would probably go on a solo mission to find Deku and take on Todoroki without hesitation.
One possible motive could be a long - held grudge that has festered over time. Maybe Bakugou's constant bullying in their past finally pushed Deku over the edge. Another could be some sort of mind - control or dark influence that made Deku act out of character.
Bakugou could use his words. He might tell Deku that he believes in him. For example, he could say 'Deku, you may be a nerd but you're a strong nerd.' It's a backhanded compliment but it shows he has faith in Deku.
One popular fanfiction concept could be Deku proving his worth without a quirk in the Bakudeku relationship. Maybe he uses his intelligence and strategic thinking to assist Bakugo in battles. For example, he could analyze opponents' weaknesses and come up with battle plans that Bakugo can execute. This would show that even without a quirk, Deku is an important part of their duo.