This is a version called the Queen's Garden which is from the Bahamas. The words are slightly different than yours. I learned it from Alan Lomax's Folksongs of North America

One day as I was going to school
I bounced my ball so high
I bounced it into the Queen's gardeen
Where no one could see where it fall

Come een, come een my brave young boy
Come een and get your ball
Oh no, oh no I can't come een
Unless my school mates follow

She showed him an apple as green as the grass
She showed him a gay gold ring
She showed him a kerchief as white as snow
So she could entice him een

She took him by the lily white hand
She led him through the hall
She led him into the green gardeen
Where no one could hear when he hollered

She brought a kerchief of linen fine
A knife both long and keen
She brought a basin of marble stone
So she could entice him een