There are regional variations in all of the ribald children's songs. This is most likely because they are learned through 'oral tradition', (ie: from kids a couple of years older), as opposed to from a written 'canon' source.I recited the whole thing, and the word "and" is superfluous.
Most likely the words to Barnacle Bill the Sailor that I learned in Montreal would have some differences from what you heard, somewhere else.