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 wanted to leave this. - Thank you. BRUCE: Rachel? RACHEL: Looks like someone's been burning the candle at both ends. - Must've been quite an occasion. - It is my birthday. I know. I'm sorry I can't come tonight. I was just dropping off your present. - You've got better plans? (..)2005 Batman Begins