If the cuts continue to not look like they are recent (as in not open at all, and you said her bracelets are off), I would introduce yourself and maybe try to find a topic or interest you have in common before you approach her so you have something to talk about (and don't do it when she is surrounded by her group of friends...girls are never truly who they are then). Maybe see if you can strike up some conversation based on prepared topic or even a class or school event.

After a few of these interactions, if she seems open to just casual chatting, I might say, "hey, if you ever want to just talk or hang out (or do otherwise specific activity) that would be cool"...but maybe put it more back on you, like say you are trying to meet new people and she seemed like someone interesting to get to know (so all of the pressure is not on her). Or if it seems like the connection is going quite well, ask her to do a specific activoty...go to the mall one day, etc...whatever you think might work for both of you.

Then you might get a better sense of her life and how she is doing, and possibly make a new friend.

It's wonderful to hear you care so much about what happens to someone you hardly know, especially since you are in high school. We need more people like you!