Being rescued is a frightening proposition for Bilbo and one that prompts him to grumble. However he soon reminds himself "not to be rude to an eagle, when you are only the size of a hobbit."
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Answered by jill d #170087
What reminds him of his low stature is the fact that he realizes without the ring there would have been no heroics. It's easy to be a hero when you're invisible.