Using “she” with gender-neutral nouns

Solution 1:

Since the phrase is "Love is a bird", the author is equating the two. "She" would refer to both.

As to why it's she as opposed to he or it, that's just a stylistic choice for the song. Using "it" would be common in everyday speech, but probably not as poetic. Using "he" would be an odd choice, since "he" is not normally used to refer to either abstract concepts or genderless objects.

This question might offer some insight as to circumstances in which you might use "she" for an object.

Solution 2:

If a mother bird needed to fly off her nest, no one would begrudge her the pronoun. If love were that mother bird, then love, too, would merit the same considered treatment as our mother bird. By saying that love is that bird, then love deserves the same pronoun.

English reserves it for unthinking, nonsentient things, usually inanimate ones. When we use he or she, we are attributing agency to the thing named. It now has a life and a soul. It makes decisions, it feels, it hurts. It is no longer an it. It is become a he, or more softly, a she.

Madonna is imputing that agency of animate life, and the delicate tenderness of a mother bird, to love itself. Of course she — meaning Madonna — uses she, for having breathed life into love itself, her it is it no longer. It is she.

Solution 3:

'[S]he' definitely refers to bird.

The line in question is a metaphor. Metaphors are all about creating connections between seemingly-unrelated ideas. Birds and flying aren't unconnected ideas, so the metaphor is either that love is like a bird, or that love needs to fly.

"Love is like a bird", then, prompts us to consider in what way are they related. What, about a bird, is common back to love? The bird has a quality that she needs to fly. '[S]he' directly refers to the bird, but is extended in the metaphor to also conceptually refer to love. The meaning becomes a prompt for us to think about love in terms of flying and freedom, and so on and so forth.

But, for kicks, let's imagine that 'she' referred to love. If 'she' directly refers to love, then being like a bird as a concept is placed completely wrong, breaking up the concept of love needing to fly. A valid sentence under that theory would have been "Love needs to fly, like a bird."

BUT, humans process why before what or how! Therefore, option number 2 is an overall less satisfying framing, being out of order for the target audience (Homo Sapiens). Assuming that 'she' refers to 'bird' is better form, because it introduces the non-trivial idea of love being like a bird before the more-obvious idea that birds need to fly.

Therefore, the optimistic assumption is that 'she' refers to the bird.