I guess you could be her friend, but if you are doing all the initating, is this really a one sided friendship?
While her and her boyfriend have broken up last week, they aren't totally over, regardless of what she says. Breaking up is actually a stage of a relationship (as crazy as it sounds) and her feelings are going to be with him still. She's not ready to be with somebody else, and yet she doesn't want to be alone. That is why they have a tendency to end up going back. Have belief in the fact that if they have been broken up, but not long enough to really change, that they are logically going to be broken up again in the future. You can be a friend through this, though you run the shot of being in the friend zone. Especially if you are the nice guy that listens to her and is her emotional tampon through all this.
If you like her as more, I wouldn't settle for less. She has a way to reach you and if she likes you and wants to talk to you, she will. Leave her be, let her drama unfold, and you may end up hearing from her. Just my opinion.
I can be a very shy guy too, so I know where you are coming from. A little confidence couldn't hurt. I get that vibe that maybe you don't have that if you need verification from others that you are good looking and a great guy. She's not the only gal out there, don't you worry, even if it's been a while.
Waking up next to a beautiful girl,
Step outside and say hello to my beautiful world.