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>Find a nice big tree or something to get behind
>Pull down pants
>Shit on the ground
>If it's only a one or two day hike, wipe with the toilet paper I brought
>Stick the toilet paper in a double garbage pack with a very tight seal
>Stick it back in my back and dump it in the trash can once I get back to the trailhead (or campsite if it's a maintained campsite with a trash bin)
>If hiking for longer periods of time, just find a tree with big, smooth, non-serrated leaves and wipe with them (if you don't know which species in your area will/will not burn your ass if you wipe with them, you're casual-tier), leave the leaves on the ground with the shit
I live in hardcore livestock country, so every open area is already swarming with cow shit. It's not like I'm doing very much damage because I'm just shitting in an ocean of shit.
As for the trash bag thing, as long as you use decent-quality trash bags and make sure to seal them tight, you shouldn't notice barely any smell, and certainly not any that will linger once the bag leaves your pack. I do keep my food in a different pocket for good measure, but considering I haven't once gotten sick while on the trail, I doubt it's really dangerous.