She was 'burning for' a chance to prove herself. [=she wanted very much to get a chance to prove herself]
('humorous') “We were talking about you last night.” “That explains why I 'felt my ears burning'.”
She was 'burning with' anger at his rudeness. [=she was very angry because of his rudeness]
(..) What did you see? A tree. There was a white tree... ...in a courtyard of stone. It was dead. The city was burning. Minas Tirith? Is that what you saw? I saw... I saw him. I could hear his voice in my head. And what did you tell him? (..)2003 The Lord of the Rings: The Return of the King
(..) as we once did, my old friend? Can we not have peace, you and I? We shall have peace. We shall have peace... ...when you answer for the burning of the Westfold... ...and the children that lie dead there! We shall have peace when the lives of the soldiers... ...whose bodies were hewn (..)2003 The Lord of the Rings: The Return of the King