There's hundreds of songs which would fit your description, except that the girl and her departed are invariably betrothed, not married. However, and this is a pure guess, I'm wondering if it could be the Bleacher Lass of Kelvinhaugh. Sample text:-

As I roved out one fine summer's morning,
Doun by the banks o sweet Kelvinhaugh;
It was there I spied a wee bleacher lassie,
She had cheeks like the roses, her skin like snaw.

Says I, "Ma lassie, where are ye going,
And what ye do I would like to know."
"Kind sir," she answered, "I am but a bleacher,
Fae Cochrane's bleach fields near Kelvinhaugh."

"O lassie, lassie, I've gold and silver,
And I would buy you silks sae braw."
"O no kind sir, it's the truth I tell you,
For I have a sweetheart and he's far awa."

"For it's seven lang years since he's gaed and left me,
And seven more I would wait on him;
O no kind sir, I would raither tarry,
And bleach ma claes here on sweet Kelvinhaugh."

"O lassie, lassie ye are hard hearted,
But such a fair face I never saw;
For ma heart's aye breakin, baith night and mornin,
For the bleacher lassie fae Kelvinhaugh."

"Dae ye see thon ships sailing doun the ocean?
Dae ye see them sailing doun the Broomielaw?
O lassie, lassie dae ye no remember,
The day we pairted on sweet Kelvinhaugh."

"O laddie, laddie I weel remember,
The day we pairted on sweet Kelvinhaugh;
Aa the sailor laddies, they aa got tipsy,
Wi the bleacher lassie fae Kelvinhaugh."

It's noo this couple they hae got mairried,
They keep an alehoose atween them twa;
And aa the sailor laddies, they aa go drinkin,
Wi the bleacher lassie fae Kelvinhaugh.