Need some advice concerning one of my best friends?

If you want to be a true friend to this girl then just sit by and wait. She seems moody and unpredictable so if you start writing messages and apologizing non-stop she might need another break from you again. Maybe be more subtle and just ask her to hang out for a day. Make sure you mention an actual day instead of just "sometime", it's easy for someone to blow off a "sometime". One thing though, I wouldn't get too attached to this girl, she seems like she wants you one minute, then nothing to do with you the next. It wont be healthy for you if you get too attached to her. I'm going through a similar situation as you, my so called best friend will ignore me for months, then come back and butter me up with compliments and wanting to hang out everyday. Then it will stop, she'll ignore me for awhile and start back up again once I've lost hope on her. I go through hell every time this loop happens. I don't want the same for anyone else. :( Hopefully it all works out for you <3 Good luck!