One interesting storyline could be a team - up against a new super - villain who has the power to manipulate time. Batman and Batwoman would have to race against the clock to stop this villain before he changes history to his advantage.
The villains in batman and batwoman fanfic can be really well - written too. For instance, the Joker. His chaotic and unpredictable nature can be delved into deeply in fanfic. Writers can show how his madness affects not only Batman and Batwoman but also the city of Gotham as a whole.
One plot idea could be them teaming up against a new and powerful villain that neither of them can defeat alone. They have to learn to trust and rely on each other's skills in a more in - depth way.
You can try fanfiction websites like Archive of Our Own (AO3). There are a lot of talented writers who post their Batman x Batwoman fanfics there. Just use the search function and look for relevant tags.
Yes, Batman Begins can be considered a mystery fiction to some extent. It has elements of mystery as Bruce Wayne uncovers secrets and faces hidden threats in Gotham City.
'Dark Victory' is another great one. It's a sequel to 'The Long Halloween' and continues the exploration of Gotham's criminal element. There's a new mystery involving a string of murders, and Batman has to navigate through his relationships with Commissioner Gordon, Robin, and the various villains to solve it.