Have you tried scolding her as soon as you see her with the bird in her mouth and saying "drop it" to get her to release the bird? That might at least start to give her the message that she is doing a bad thing. And, knowing how sensitive Goldens are, if the bird is still alive, and you showed it some caring, she might realize this is another animal, and not a plaything.
I suppose as a last resort you might get a warning bell for her collar, as many cat owners do.
She sounds like an incredibly fast girl - have you considered agility training for her? It might be fun for both of you, and give her a different hobby than bird-catching!