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]
(..) Thought you said no one says "blog" anymore, huh? Bye, Fred. Goodbye, Mrs. Finnerty. Oil painting by Tom Freeman to commemorate the burning... ...of the White House by the British in . - Wait, the White House burned down? - Yeah, yeah, in the War of . Practically had to be rebuilt (..)2013 White House Down
(..) ...and you were wounded in the Kunar province. - Yes, ma'am. - You received a Silver Star... ...for pulling a Corporal Dawson from a burning Humvee? There was an IED attack. Humvee flipped, we were taking fire, so I grabbed him. - Why? - I was a little concerned... (..)2013 White House Down