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]
(..) - The air vent. Open and all's well, closed and you're not to enter. And the microphone? Peter? The boy stood on the burning deck whence all but he had fled The flame that lit the battle's wreck shone brightly o'er the dead 'Beautiful and proud he stood as born to rule the storm (..)2011 Tinker Tailor Soldier Spy