If kept in a paper bag, bread will become dry and stale after a couple of days. If placed into a plastic bag, all the moisture is retained, the crust looses its crunch, and the bread is as disappointing as if it was stale. By keeping the bread in the paper bag it is purchased in, and inserting that into one of my linen pillowcases, moisture is retained but the bread can still breathe. I find it stays fresh for about 5 days when I do this. I don’t know that linen is superior to plain cotton for this use case (but I do know that linen is superior to plain cotton for sleeping on).
Apparently you can buy linen bread bags made explicitly for this purpose, but I prefer things that are multifunctional, and I already have a good set of pillowcases taking up space in my bedding box. The small size of my pillow means that I can just squeeze two normal sized loafs of bread into a single pillowcase. To store a baguette I first cut it in half.