Preface: I am scanning "Bedroll" posts before I post my own question.
Your local house paint supplies store sells canvas drop cloths. Buy a 3m x 4m (9x12 here in teh colonies).
Interleave two blankets of your choice, one in the other: Half of one, half of two, top of one, top of two. (I scored a half-dozen US Army Medical blankets from the source mill. Bwa ha ha.)
Center the blankets on the tarp, long to long. Put the bottom of the blankets a hand-length or two from the bottom of the tarp. (Pro-tip: use a couple blanket pins to hold the blankets together at the foot.)
Fold the tarp sides across the blankets, following the interleaving pattern. Or not, your choice.
Roll from the foot-end and tie with the material of your choice. I use five-strand jute garden twine but I dream of leather straps (for carrying the bedroll. What where you thinking?).
Optional: coat the bottom, or all, of the canvas with a waterproof sealant of your choice.
Optional: use a hematite-based egg paint to "waterproof" the canvas. That's more period-specific. "WaterSeal" is silicone-based, not period-specific, is slightly more fire-resistant than raw canvas, and works well. [Wish I had some.])
Use: One sleeps with one layer of blanket on top, three below. Scrape trenches for one's shoulders and hips.
The extra length at the head of the canvas can be configured into a head-tent or head-awning.
Use the blankets alone on a bed of local insulation material and sling the canvas in a variety of pitches. (This part is where I get my enjoyment.)
Disclaimer: NONE of this is original. Most of it came from my '60s Boy Scout Handbook.