Okay, I don't know much about Batman canon, so I'm just going based on what you have here and some limited knowledge.

But if you were thinking of making her, say, a muggleborn to fit with her original origins, you could make it so that she found out she was a witch, and a family friend of her dad/or neighbor could be some crazy wizard guy who lives not exactly on the right side of the law. If you want to avoid the kinda incestyness, that is. He could have seen her do accidental magic in her backyard and took her under his wing. If you want him in and out of her life, he could move away or what have you.