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]
(..) - Actor #: That's an idea. - Actor #: What is? Wouldn't it be dramatic? Supposing the people inside were dead, all stretched out with the lights quietly burning about them. I'm sure it would be very amusing. Man: Why you ask? Why is not the question. How? Now, that is a question (..)2003 House of 1000 Corpses