Here's another children's rhyme that mentions "bra"
Group                Bang Bang Choo Choo Train.
                Watch Kadisha* do her thang.
Soloist #1        I can't,
Group                Why not?
Soloist #1        I can't.
Group                Why not?
Soloist #1        Because my back is aching.
                My bra's too tight
                And my hips keep movin                                                from the left to the right.
Group                Her back is aching
                Her bra's too tight
                Her hips keep movin from                                        the left to the right

* personalize name
[This is a foot stomping cheer that I collected from African American girls in Pittsburgh, PA area,1999}

Somewhat like Guest's Dec 2, 2004 rhyme, when I was growing up in Atlantic City, New Jersey in the 1950s we jumped rope to "Postman, Postman do your duty/here comes Debby*, an American beauty/she can wiggle/she can wooble/she can do the split/but I betcha 5 dollars she can't do this.
We would then do actions and chant "lady on one foot, one foot/one foot/turn around/lady on two foot/two foot/two foot/touch the ground etc {it would continue with lady on three foot meaning two feet and one hand on the ground, but I don't remember what the rhyming word was. It ended with lady on four foot {both hands and both feet touching the ground and we would say something like "jump out now", This was said if the person jumping had lasted that long without missing,which I usually didn't.

In the 1980s Pittsburgh, PA my daughter and her friends used the African booty line. "African booty" means "big butt"-and is a compliment. But my daughter and her friends said, "She can wiggle/she can woogle/she can do the flips {or "she can do the splits"}. And they didn't add the "lady on one foot" parts.

I think we had more fun way back then.