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]
(..) Because I get a little scared in the dark sometime... ...if it's a strange place. It stays pretty bright around here all night long. We always keep a few lights burning out in the corridor. The corridor? Right out there. You can sit. I couldn't help it, boss. (..)1999 The Green Mile