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]
(..) He's a sniveling little sycophantic tushie kisser, and I hate him! He weasels his way into every area of my life. The good thing about the Independence Inn burning down... was that Tobin was gone, but yet, here he is, back. - He's like the cat. - What cat? The one that came back the very next day. (..)2004 TvShow: Gilmore Girls Title: The Nanny and the Professor Season: 4 Episode 10