You would never see friend-bird. It would always be written as bird-friend - a bird who is a friend. There is no logical reason - it is just what has developed as accepted usage. By the way, a human friend of birds would be written 'bird friend', without the hyphen.

This question of "bird-friend" made me laugh because it reminds me of when people try to choose between the words girlfriend vs. friendgirl. Typically a girlfriend is a female that you are in a relationship with, though some women use it among themselves as a term of endearment without romantic connotations. To avoid this, some people say "friendgirl", making it clear that the girl is just a friend. (This can be done with boyfriend vs. friendboy too). It's an informal saying. So, the only time you would need to say "friend-bird" is if you were making it clear that you are not dating the bird! Are you reading a teen bird drama or something? It would work there. Hehe. Otherwise, "bird friend" is right to mean either a human friend of birds or a bird that is a friend. And about what fdmaxey said about the difference in writing between "bird-friend" and "bird friend", from my view the - doesn't disambiguate the two possible meanings. Hope this helps!