I used to allow my U2 onto my shoulders, he's never bitten me but has almost taken an ear off of my husband. I've decided to not allow him anywhere close to my face! Needless to say, my husband doesn't allow him anywhere close to his body...period! They communicate from afar!
I had a cockatiel years ago that "lived" on me whether it was my head, shoulders, chest or lap. He would nip once in awhile, I called them love bites. My U2 has surgical instruments attached to his face!