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]
(..) Big banks, small bank... I like to make money. Alright... Let me put it this way.... I'm standing in front of a burning house, And I'm offering you fire insurance on it -How can these underlying bonds be... as bad as you say? It wouldn't be legal! Nobody knows what's in them! (..)2015 The Big Short