I would not call it a shooting bag or pouch, which generally has only what you need to shoot with: ball, patch, caps or spare flint, and *maybe* a couple of tools. You shouldn't have to dig through a bunch of items you don't need to get to what you do need to load and fire.
I guess it also depends on what your persona would need. If you are in battle, you aren't going to worry about having the tools to field strip your gun immediately at hand. They will be in the bottom of your haversack/knapsack or back at camp. If you're a trapper, you might have it all in one bag, or leave the seldom used stuff with your camp or on your mule.
What do we call those bags? Are you out there strictly for fun, or portray an aspect of history? Although "Possibles" seems to be a modern term, I personally don't find it obnoxious. If someone is making an effort to portray an aspect of history, perhaps it would be better to refer to it as a hunting/day/game bag, depending on the portrayal.