Lol they did have sheet-like bed linens in classical Greece but probably not silk. I think it was linen or wool. The wool isn't exactly a titillating idea but the linen might be okay.
Also, to the author, yes the pro-Sparta stuff is annoying and spreading, don't mind it being taken down a notch myself. I prefer Athens, and even they are over-hyped at times, but nothing like Sparta.
I've been thinking of it as the woven, shedded skin of her hair-snakes, since the island where she lives is barren (no flax for linen or sheep for wool). Since it's a made-up fantasy fabric, I can give it just about any texture I want. I have no idea if I'll include that detail unless I find a good way to work it into the dialogue.