I believe the bird is significant because it represents a part of nature which is disturbed when the traveler shatters the silence by knocking loudly at the door. In keeping with the theme of the poem, the scene in the wood is quiet and placid - "the horse in the silence champed the grasses of the forest's ferny floor", and the lone house with its spirits within is shrouded in silence, at peace with the wildlife around it. The traveler, with his loud, imperative ways is an encroacher, incongruous in the serenity of the natural world. The bird, startled, flies "up out of the turret" when the traveler breaks the silence by calling out loudly, "Is anybody there?", and rapping sharply on the cottage door.
The bird might also be significant because, by its presence, it provides the answer to the traveler's question, "Is anybody there?" There is, in fact, no one there, no one from the world of men, at least. The cottage is completely given over to nature, uninhabited, it is a part of its idyllic surroundings. It is at one with the forest and the wild things that inhabit it. The birds and other creatures live there in their natural state, unmolested by the discordant ways of men.