[mom of 3 dogs]

i think it really would be amazing if you found the actual owner. Birds can fly for very long distances, so it highly possilbe that birds owner may live no where near you.
Would be good if the cockateil was an unusual color. The common colors are the normal greys... they pretty much all look alike. then the latino colored , which are a real pale yellow with the orange cheeks. , but if its a pied that would be more easily identified ,
Dont tell rescue what color the bird is and ask when you speak to owner what color.

If you cant find the owner , i think it would be fine to place bird with a good owner who will care for bird. , someone who really knows how to take care of a bird. alot of people dont know how and because of that the bird will die. like catching a draft, birds are very senisitve to that and can die from a cold. or certain fumes that are normal household fumes, like roomsprays. and should be fed certain things ... i never lost a bird but have heard many stories.