I have mulched them with straw but not simply covered with straw…I don’t see why it would not work. I plant lots of things in bales of straw. (Decomposed straw would work better than a bale I would think?

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my understanding of taters is as
@Scm shared diagram…so long as keep covering potatoes branch out as the plant grows up…so keep covering with soil. I know people that lay on ground, put tire around and fill with soul. As play grows, add another tire on top and fill again with soul and so on…when time for harvest they knock the tires over and don’t dig.
I hill my taters with a garden bedder. I have a walk behind manual push as well as a bedder for the tractor. The manual push version doesn’t make very tall hills and I don’t think that would get you much…it’s fine for beans and such but only hills a couple inches high. The bedder on the tractor makes a much larger hill and when need to add more soil just run back over your row of taters and pull the soil in and up. It works pretty well IMO.
I’ve only used straw over taters to suppress weeds and hold moisture. I would think you could try a bale of straw easy enough…here is the recipe I have been using with straw for several years with success(for other plants - not taters)…
Find out how to grow vegetables in straw bales, an innovative gardening method that’s ideal for poor soil conditions.
hgic.clemson.edu
if only want a couple plants, I think the old tire method would be the way to go.