The common verses in "Farmer's Curst" about the woman climbing or mounting the devil's back may come from 'A Pleasant new Ballad you here may behold How the Devill, though subtle, was guld by a Scold' when the devil takes the form of a horse.

According to Ashton:

The story of this ballad is, that the Devil, being much amused with this scolding wife, went to fetch her. Taking the form of a horse, he called upon her husband, and told him to set her on his back. This was easily accomplished by telling her to lead the horse to the stable, which she refused to do.

'Goe leade, sir Knave, quoth she, and wherefore not, Goe ride?
She took the Devill by the reines, and up she goes astride.'

And once on the Devil, she rode him; she kicked him, beat him, slit his ears, and kept him galloping all through Hell, until he could go no longer, when he concluded to take her home again to her husband.

'Here, take her (quoth the Devill) to keep her here be bold,
For Hell would not be troubled with such an earthly scold.
When I come home, I may   to all my fellowes tell,
I lost my labour and my bloud, to bring a scold to Hell.'