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]
(..) That's it. I have done it to her countless times. And usually, she would have caught it without burning herself. So why didn't she this time? I don't know. She seemed distracted lately. What do you mean distracted? Um, leaving early, you know, (..)2015 TvShow: Bones Title: The Promise in the Palace Season: 11 Episode 7
(..) All right, you got it all wrong. Uh, really wrong. I pulled a few pranks. We all do that. Burning someone is a prank to you? She wasn't supposed to get burned. Oh, so it was her fault? All she was supposed to do (..)2015 TvShow: Bones Title: The Promise in the Palace Season: 11 Episode 7