It's only natural to have an extreme trust in someone who saved you from yourself. Granted she didn't stop the knife, but she did come and get you when you needed someone. That says she was already ready to take that first leap and trust you as well. What I find odd is how ridged people keep their relationships. You talk like if you don't choose to persue a serious relationship, it'll never come to fruit. From my own romantic experience, things develop on their own whether you filed the person as a close friend or significant other material.
Personally, I filed the person as a punching bag and now, three years later, I'm engaged to him. Funny how it works, eh?
ANYWAY you need to have this converstaion with her. We can advise and say yay or nay, but the truth is she is holding all the cards in this. Don't pounce on her and be like OMG I LOVE YOU, but a nice night over at your apartment with a movie, popcorn, and some lounge time on the couch to just lay around and talk won't hurt. Just bring it up simply that you see things possibly going places, and simply wanting to know where she stands. Don't be like PLEASE GO OUT WITH ME, or something else that forces a cement decision, do it more as a status-check. "Hey, I feel this way. Are you on the same page or somewhere else?"
It's a converstaion that's tough to have, and people like to jump to conclusions in the middle sometimes. It's best to just buck up, put yourself out there, and remain calm no matter what turn it makes.