However, it is not the case that God becomes a bird. If we read the scriptures carefully we see the following scenarios:
The Holy Spirit is said to be LIKE many things in scripture including flame, winds, and a dove. We need to look carefully to see what the scripture really says:
From the Baptism reading:
After all the people had been baptized and Jesus also had been baptized and was praying, heaven was opened and the holy Spirit descended upon him in bodily form like a dove. And a voice came from heaven, "You are my beloved Son; with you I am well pleased."
It doesn't say that the spirit 'took the form of a dove" it says that the spirit descended upon him LIKE a dove. So we don't know what the spirit's form looked like only that it was flying apparently.
The dove is a symbol in ancient times (read jewish culture) of the predominance of spirit over matter. Thus they were also the poor man's offering to God. People brought doves to the temple when they couldn't afford anything else as a sacrifice--again symbolizing a spiritual offering as being dominant over material wealth. It was therefore also a symbol of freedom for the poor--our offering is as good as someone who gives 1000 shekels.
So the symbolism the author is using here is rich indeed...
God offers Himself to us--Jesus though hidden in this material form is really God incarnate. The spirit of his essence dominates over the material human form.
It also symbolizes that the simple carpenter's son is more than meets the eye--the dove points us to that.
Moreover, Luke is writing to a Greek audience and the dove was perceived by the Greeks as Aphrodite, the goddess of love and beauty, and thus also invested with erotic connotations. As an attribute of the fertility goddess, the dove became a symbol of love between human beings, and between the deity and the worshipers.
So here we have Jesus who is God become man, we see the interplay between man and God. The dove, a female symbol is juxtaposed with the male voice that offers this new creation as part of the self-offering of God--the result of a male-female union of the divine. The Holy Spirit comes to the virgin through the Father and the result is the union of God and man. The Spirit literally embodies in a female to produce the male Jesus.
In general, the dove has become the symbol of the holy spirit (which often in modern culture takes on a female connotation) and quite often it is used as a symbol of peace, dating back to the Old Testament when God sent the dove with the olive branch in its mouth as a sign of peace and covenant.