It seams I was mistaken, the song I'm thinking of is not My love, wich is a traditional you cheated on me song. The song I'm thinking of is actually A Maid In Bedlam. My querky memory was right about who I heard sing it though. My source for this song is Atwater-Donnelly on their album Culled From The Garden.

A Maid In Bedlam

Abroad as I was walking
One evening in the spring
I heard a maid in bedlam
So sweatly for to sing
her chain she ratteled with her hands
and thuss replied she

ch.

I love my love
because I know
my love loves me

Oh my cruel parents
are being to unkind
they drove and punish me
and truble my mind
for though I'm ruined for his love
contented will I be

ch.

Would I become a swallow
assend into the air
and if I last my lover
and could not find him there
I quikly would become a fish
and search the flowing sea

ch.

With straw I'll make a garland
and dress it very fine
I'll mix the wame with roses
lilly pink and tyne
I will preserve it for my love
when he returns from sea

ch.

Just as she was sad weeping
her love came on the land
hearing whe was in bedlam
he ran straight out of hand
and as he entered into the gates
he heard her sie and say

ch.

He stood and gazed on her
hearing his love complain
he could not stand any longer
he bleed in every vain
he flew in to her snowy wite arms
and thuss replied he

ch.

I hope this is what you'r looking for. The course is only slightly different.