I think that in modern times Ava is normally simply a respelling of Eva to force English speakers to use the "continental European" pronunciation of that name.
However, Ava was also used in medieval times as a short form of various Germanic names containing the root av, (which is so ancient it is of unknown meaning), and it's possible that some examples of women named Ava during the late 19th century were revivals of the medieval name. There was a St. Ava (also called Avia) who was an abbess in the 9th century in Hainaut, which is today a Belgian province.
The "like a bird" meaning comes from people confusing Ava with the Latin word avis, and the "bearer of good news" derivation would come from assuming it's a short form of Evangeline. Both of those seem like unsubstantiated guesses to me. "Bearer of life" seems to be a metaphorical meaning based on Eve, not an etymological meaning. I have no idea where "serpent" would come from! :)