[Inferred from the gerund bird’s nesting, which was much earlier in use; cf. nutting, to nut, etc.] intr. To search for bird’s nests.

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1856.  J. Grant, Black Drag., xlvi. A thicket of fir-trees, in which I had often bird-nested.

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1875.  ‘A. Hope,’ My Schoolboy Fr., 148. They went to birdnest in the morning.

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1877.  [May Laffan], Honourable Miss Ferrard, II. ii. 227. A solitary magpie, birdsnesting, uttered its hoarse, vindictive screech, as it sailed clumsily overhead.

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