I've had a couple of people ask me why Edward didn't call the police when he rescued Isabella. Yes, for most people that would be the logical choice of action. So what is Edward thinking? Why didn't he? There are two main reasons why he didn't call the police after he rescued Isabella.
First, he is a very private man, but he is a very public figure. Given his lifestyle choice and his position in Seattle society, he's learned that the less people know the better. And with Isabella, this is even more important. He doesn't know exactly what he's dealing with, why she was where she was, nor how she got there. Edward put his proverbial neck on the line by going to Aro and buying her. He doesn't want that kind of information to become public knowledge.
His second reason for not involving the authorities, is because he doesn't think that would be a good choice for her right now. Isabella is very submissive right now. If she was put into a high pressure situation, she may lose it entirely. And what would happen if she was pushed into pressing charges? One look at Aro, or any other dominating figure, especially male, and she'd back down if not collapses into herself.
I've also had several comments on Edward's thoughts about her becoming his submissive. Again, there are a couple of reasons for that, but they are pretty simple.
1) She is already trained. As sick as that thought might be, Aro did train her to be submissive. It is only her fear that ever makes her hesitate. Take that fear away, and Edward knows she'd be perfect.
2) He's attracted to her. We all know Edward thinks Bella is the most beautiful woman in the world. That doesn't change here. He wants her, plain and simple, but he wants her to want him as well.