Here's a children's rhyme that mentions "fat bums":
   
Apple on a stick makes me sick makes my heart beat 2-46 not because you're dirty not because you're clean not because you kissed the boy behind the magazine hey girls you wanna have some fun cause here come a lady with a big fat bum she can wibble she can wobble she can even do the splits but i bet ya i bet ya she can't do this close your eyes and count to ten if you muck it up you're a big fat hen. 1-2-3-4-5-6-7-8-9-10 (if you didn't muck up) we didn't muck it up so that's the end. we're best friends. (if you did muck up) we mucked up and that's the end so start again cause we're not best friends.
-Allie; 2/15/2007

-snip-

That example was sent to my website Cocojams . Fwiw, I just posted that example and some others to Mudcat's thread on Children's Street Songs thread.cfm?threadid=4300&messages=133 in response to a guest's query about that rhyme.