Bee Bee Bumblebee

Found in Journal of American Folklore, Volumes 30-31, published in 1917. They mention a Bolton text, so I went to look for it.

Found in The Counting Out Rhymes of Children by Henry Carrington Bolton, published in 1888. This seems to be the oldest existing source.

Also researched in Counting-Out Rhymes: A Dictionary, edited by Lois Rankin & Roger D. Abrahams, published in 2013.

Then I went to research the sources mentioned above. Below is the JAF - Journal of American Folklore, published in 1918.