Following on from the 2 posts above, I remember this version from when I was at school in Hong Kong in 50s/60s:

Ohh her washing was known to the whole of the country
From old Donegal to the borders of the Bantry
And women and children from every far county
Were singing the praises of Biddy Malone.

She was spruce, she was spry and she always would try
To help the poor folks in the villages by

And there in the evening she sat at her door
with tales of her washing and (sounded like) rory o'moore??