Somebody wrote the lyrics in, or no later than, 1939:
“Created in or around the year 1939, Wheels on the bus is inspired from famous British children’s song ‘Here We Go Round the Mulberry Bush’…” https://kidstvofficial.wordpress.com/tag/wheels-on-the-bus-song/
“‘The Wheels on the Bus’ is an American folk song dating no later than 1939 written by Verna Hills.” https://en.wikipedia.org/wiki/The_Wheels_on_the_Bus
“…written by Lydia Ulsaker.” http://www.sheetmusic365.com/t/page/3/
“…a song known already in 1939 (published in the American Childhood magazine, vol. 25).” http://www.singing-bell.com/the-wheels-on-the-bus-nursery-rhyme/
The wheels of the Greyhound bus shown here are not going ’round and ’round at this stop in Victorville, CA on its way Los Angeles. The Frasher Foto, a business in Pomona, postcard is from http://content.ci.pomona.ca.us/cdm4/item_viewer.php?CISOROOT=/Frasher&CISOPTR=1518 via http://mdhcaexhibits.blogspot.com/2013_05_01_archive.html .