Have you thought of a slingshot. Up here there is always an abubnance of squirrels, marmots, grouse, ptarmigam etc. The birds in particular are about as dumb as a cow and can be approached very closely. A well placed shot that although may not kill the bird, will stun it enough so that you can finish it off.

A decent slingshot along with a tube of 1/4 or 3/8 ball ammo and an extra sling should set you back less then $30.00.
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Earth and sky, woods and fields, lakes and rivers, the mountain and the sea, are excellent schoolmasters, and teach some of us more than we can ever learn from books.

John Lubbock