too bad... i think she's just making things smooth for you. If she's the one who initiated the break up, it's normal that she says sorry. because of course she still cares about you and she's thinking she might have hurt you.
i suggest that you don't much of your emotions with her apologies, just act cool towards it because it seems like it does mean anything at all. im sorry to say that.
as you said, maybe she just wanted some time apart to make herself want you back. so best that you can do is give her the time she needs. for the meantime, just make yourself busy with other things. You can concentrate to work or join a new sport. It's important that you get a life also!
because girls like guys who are not too clingy. Girls nowadays are becoming more independent and we also want our man to become one. Plus, if she really has no plans of getting you back, that'll make moving a little easier..right? so good luck!