I'm going to hit your last point first, since it's the main reason for your "reluctancy."
It's very damaging psychologically when a girl breaks up with you. It sucks. It burns. It eats at you and challenges your faith in humanity. But you have to move past these bad feelings sometime; dwelling in the past won't help you with any relationship in the present or future. You have to learn to trust people again, even when you know you might get hurt. It's not an easy thing to do, I understand that, but without your full resolution to be committed to her, and without your trust in real relationships, your asking out of her will be MUCH more difficult, and it may even be harder to maintain the relationship when you're so worried about her leaving you that it's what she does. Self-fulfilling prophecy ftl.
On the other hand (sadly I must show you both sides of the coin here as a friend), you're young. Hormones are crazy. You can like someone for the wrong reasons, even label your latest attraction as "the one" for the tenth time. Relationships at this stage in life aren't meant to be eternal (very very few work out that way for many reasons), so you shouldn't go into a boyfriend/girlfriend committment thinking that you'll definitely stay with this girl for a few years. Circumstances, and more imporantly people, can change.
Ok, I know that ending was abrupt, but I think I covered both sides well enough to move on to getting at the questions/situations.
Ask her things like how she would feel to have a BF (it has to be kinda led up to though in some other conversation, do it kinda subtly though so it's not too obvious). Btw, if she asks, just tell her that you're just wanting to know. It's the truth, and it doesn't directly tell her you wanna go out. Half-truths ftw.
Maybe you could ask her what she thinks about a BF/GF relationship, or ask how her last serious relationship went.
Does that help?