22 year old Bruce Wayne returned to Gotham City roughly two years ago. One year ago, the masked vigilante known as Batman started terrorizing the criminal underworld of Gotham. Bruce's goal is to take his resources and training to inspire to people to retake their city and pull it back from the brink. In many ways, it is working. The police are becoming more bold and the criminals are taking steps to evade the Batman's attention. In other ways, however, Batman is starting to become a victim of his own success. There have been a number of copycat batmen over the last few weeks, and it is becoming clear that these individuals are a huge threat to themselves.
The most prominent copycat is your character. While Batman wears a advanced kevlar combat suit, she wears spandex with a few homemade weapons. She has had some success against muggers and things of that nature, but on the night Batman first meets her, she has taken on a powerful criminal and gotten herself captured. The criminals don't kill her out of fear of attracting the bat, but she is bound, gagged, and being threatened when Batman shows up and rescues her. Batman warns her not to try something like this again, but finds her a few days later in a similar predicament.
I think it would be fun to play a game between Batman and the woman who is trying to help him, whether he wants that help or not. The woman could be Batgirl, a female Robin, or a completely original character. I would like to play out her being a damsel in distress at the hands of her enemies, until Bruce eventually has to train her for her own good. Once they are master and apprentice, romantic sparks could start to fly, as she is the only one who really understands his desire for justice, but at the same time, her developing skills leave her prone to capture and distress.