The version I grew up with (which has a slightly different cadence) takes a much darker turn. It describes the perspective of a Medieval girl who is being forced (likely by her father) to marry someone she doesn't love; to avoid this, she kills herself on her wedding day:

Rose, Rose, Rose, Rose
I will live to see thy wed.
I'll be married at MY will, Father,
at my will.

Ding dong, Ding dong,
wedding bells on a September morning.
Carve my name on a moss-covered stone,
on a moss-covered stone.

Mother, Father, dig my grave.
Dig my grave with a golden spade.
Bring my friends and a white turtledove
to show I died for love,
to show I died for love.

-