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]
(..) I'm gonna go up and pull... Here... Hold it. Enough of this shit. We'll never make it across land this way. He is burning out captain. Captain you ain't doing us nor him... ...no favor... going on suffering like this. Captain! Captain, it's all the same up here. (..)2015 The Revenant