This Scots dialect tale has more in common with 'Three Golden Heads' than others with the 'Well at the World's End' (and similar) titles.
Here the bonny king's daughter arrives at the well and it is too deep to dip the bottle in. "Three scaud men's heads" ask her to wash and dry them with her apron and she does so. They then dip the bottle in for her and also confer wealth and beauty upon her.
The ugly queen's daughter is then sent but refuses to wash and dry the men's heads. She is made even more ugly and blighted with further afflictions.
What is going on here? Is this a fertility theme? In George Peele's 16th century play which employs these folk-tale sources, the verse reference:
Fair maid white and redrefers to a bawdy term at the time where "kneading cockle bread" was a term for female masturbation. The actual reference seems to be to the fact that the maid will get a husband. This is the case with both daughters here, though one gets a prince and the other a poor cobbler who beats her. Does each girl have to confront maleness in order to make the transition to marriage? If so it is simply a variant on the 'kissing the frog' theme which is linked to the other 'Well at the World's End' stories.
You shall have some cockle bread
This is an aspect emphasised, also, by the fact that each of the girls is offered a ride on a pony "over Hecklepin Heath" on the way to the well, but only the 'bonny' daughter accepts the ride.