'[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.