You are not a murderer.
You ended the life another forest creature just trying to live and survive like you were. And like how the baby bird tried to live and survive.
You murdered just to lose the baby bird.
It is gone. Whether lost to the elements or just another coyote, you will never know.
But you tried. You sacrificed your innocence for the sake of a random, helpless creature, and that was a very nice gesture. You also put a rock on a baby bird to keep it warm, so your choices, reasoning, and judgment are strange but in the right place and for the right reasons.
At least you tried, bear. At least you tried.