http://www.youtube.com/watch?v=sng_CdAAw8M , at about 0:53.
I am not sure which word I hear. I am hearing something IN BETWEEN "belly" and "barely."
I think it is "belly," but the vowel sound she uses is somewhere in between the "eh" of "bell" and the "ay" of "bay."
I don't hear any R.
I'm not sure what the "official lyrics sheet" would be. I have noticed that Internet lyrics pages are, VERY often, OBVIOUSLY transcriptions by people listening to the words and contain errors. In song lyrics, where the words are evocative and poetic rather than logical, context is a weak guide. The singer may distort pronunciation as part of his or her style. And trained singers are actually TAUGHT to modify vowel sounds and pronunciation in ways that sound better musically. The extreme case of this is the dying tradition of singers being taught to use Italian vowel sounds when singing English! But in any case singers like to open their mouths wide, and prefer big open vowel sounds.
I think the "eh" in "belly" is a little constricted, and when she, as a singer, stretches it out, opens it, and sort of flirts with it, it sounds like "ay." And then, given a choice between "Bailey," which isn't a likely word, or "Barely," which is, people hear it as "barely."