Congrats on your purchase ! Make sure you read all you can about Ekkies, they have specific needs and traits, but they are good companions.
You can also check out this forum :
http://eclectusparrots.net/forum/And make sure you subscribe to Laurella Desborough's daily letter (google her name, you'll find it). She's a worldwide authority on Eclectus.
READ, READ, and read again.
As Onionglass said, Eclectus do not naturally like being petted. This is something they have to learn and even then, it will be on their terms.
I got my male at 4 months old. He bit me for at least 3 weeks. It was out of fear. He has not bitten me since. He " feels me " with his beak a lot, but not to hurt.
I would say let her come to you when she's ready. Talk to her, sit next to her and read outloud, sing, do whatever you like, but don't force yourself on her. She should want to be near you real quick !
Ekkies really like to be with people, even if it's not to be petted, they need company. Mine will sit on my shoulder all through a movie. He flies to me when the movie starts and stays there the whole time. He follows me around the house as well. He's almost 10 months old now.
Take your time, that's your best advice.
Good luck !