A sparrow is a bird that is referred to in the Gospels by Jesus as a symbol of a life form that is worthless in comparison to a human. Jesus deliberately points out the sparrows in Chapter Six of the Gospel of Matthew as a lesson in how God cares for all of his creation. If God cares for such an insignificant bird as the sparrow, how much more will he care for man? The sparrow is therefore an example of a bird that is very tiny and unimportant in God's creation. It is particularly relevant that Bede compares a man to a sparrow in order to emphasise how unimportant man is and how brief his life is.
A good overview of sparrows (and many other birds) mentioned in the Bible can be found here: http://www.studylight.org/dic/hbd/view.cgi?number=T946
Here are some relevant passages from this source, with my comments, in italics, about the possible appropriateness of the Biblical references to the story told by Bede:
Psalms 84:3 refers to the nesting habits of the sparrow at the altars of the...
(The entire section contains 5 answers and 611 words.)