In my experience, practically bedsheets are made of cotton. Perhaps there was a time past when they were made of linen – but in my experience, while linen is a good enough fabric for outer clothing, I wouldn’t want to sleep on it. Would you?
They still are, though:
http://www.cuddledown.com/dept.asp?cid=108&cn=Linen&srccode=hng0015
Well, that’s why they switched to cotton, no? You’ve got to remember that cotton is a relatively new product in Europe compared to linen. No one had cotton, so they made use of other fibers. Like, say, linen. The material got attached to the implement, and so today you can have cotton linens, plastic glasses, graphite pencil leads, and steel silverware.
General info on linen. As cher3 said, they do still make bedding cloth out of true linen.
It’s quite nice to sleep on, not rough at all.