Unless you're a swallow
A swallow is a type of bird, which ties in with the previous line about Birdman.
Thus, only two ways he is calling that girl “Baby” :
She’s a swallow => a “birdwoman” => rapper Birdman a.k.a. Baby being the only person he calls that.
Or she swallows after giving him a blow job.
To help improve the meaning of these lyrics, visit “Berzerk” by Eminem Lyrics and leave a comment on the lyrics box