Mostly, the old Eagle dragbag/mat (DB-BS, the "Sniper Rifle Case and Shooting Pad") that I transport the bolt rifle in. One of the best things they ever made, if you find one in good shape in the back of the arms room or surplus store, get it. If you have a sewing shop, update materials a tidge maybe, and clone it.
If permitted,
detailed writeup from 10 years ago on SH. Here's mine in use a year or two ago:
Supposedly they accept shoulder straps as well, but I've never gotten how exactly.
My more portable/ad hoc solution is this comically lightweight Matador pocket blanket.
https://www.amazon.com/Matador-Blanket-Version-Camping-Resistant/dp/B06X6GY8GS I got mine with a subscription outdoorsy service, so it is sadly red, need to get a green one (or a black one) so I carry it more often instead of worrying about the red. It is about the size of your wallet, weighs less, and is so thin it seems like it'll blow away (in fact, it will... comes with stakes in the corners) but is some odd material that isn't just tear resistant, but is poke-resistant. I've laid on it comfortably on fairly new crushed rock (gravel). No idea how, but interesting.
The name is silkscreened on with something not suitable, it melted and stuck to everything when I tried to Permethren it. So, test that when you get one, then have lots of denatured alcohol and rags around to remove it entirely when it does melt; but I do have hope they've fixed that.