By far most of the places we camp, especially in the national forest, are into some types of recycling. And I gladly sort out the stuff. For sure there's always a main trash container even if recycling is not an option. One place I like to go in the western NC mountains has the bear safe trash recepticales and there you just mix everything in one bag, which usually for us is one of those grocery plastic bags. And we most generally start the campfires (or at least burn) the paper products, like a cereal box, paper towels and such ... never plastic or something that will not completely burn up. Also, in known bear country, usually do the trash after every meal - never leave some type of eatables, like potatoe peelings, left over food stuffs, a bone .... all goes to the trash A.S.A.P.
Have had one big ole bear come right into our site while it was still daylight. We yelled at him/her and although it left the site, was not into a real big hurry about it.

We have a couple collapsable mesh cubes with handles from Wally World. Put the returnables in one and the recyclables in the other. They can be hosed out easily and dry quick, the added bonus is thst they fold up flat for storing in the camper .

We always have a second bag for the cans and bottles.  Just trying to do my part to make a difference.