How to handle girl out of my league

B.S.  If she REALLY wants to make time, she could and she would. It is that simple.  

She is probably used to people chasing her around and she just wants to add you to that list IMO.

Either just let it go or give her the old, "I'm interested and I know you have a lot of obligations, but you have to meet me half way if you are interested in getting to know each other better."

Then let her put her money where her mouth is...you'll get your answer quickly.  If you think you can carry the water for the both of you until her schedule lets up and things get more manageable, you're kidding yourself.  Took me over 40 years to learn this.  

I went to a fitness contest on the beach once in Florida and struck up a conversation with the absolute hottest girl there.  I couldn't believe how insecure she was.  It was amazing.  She could have walked into the Playboy mansion and she would have been put in the magazine on the spot.  But her self esteem was lacking big time.  I couldn't understand it.

But a cake is so much better...  it has frosting, which you use to personalize it with a message or lick it off of the object of your desire.   I think it's time to amend the Covers Constitution of Courting Women