Of course, they carry a measure/charger everywhere they take their gun. The little thing weighs practically nothing. Some guys keep a measure in their shot pouch. I prefer to tie my measure to the buckle on the strap of my shot pouch. That way I always know where it is, and it is ready for use at all times. It hangs down on my chest when the bag is hanging over my shoulder. To keep it from flapping around, I tuck the measure into my shirt.
Forget about anything you see in the movies! They are generally fantasy.
I have a couple of the commercially made brass powder measures, but it is not difficult to make your own from a section of antler, bone, river cane, a piece of wooden broom handle, etc. Right now, I use one that I made from the femur bone of a deer. Inside my pouch I keep a spare that I made from an antler.
To make one you probably will need to start with an accurate way to measure your preferred powder charge. You can use a commercially made measure, or a powder scale. Then take your antler tine, bone, or whatever you want to use to make your measure, and drill down to hollow it out. 3/8" or 1/2" drill bit works for me. Pour your measured powder charge in the hole and mark where it tops. Pour out the powder, and then cut off the measure at that spot. If you want to make a little pour spout, then cut the measure off a little above the powder line and carve it to your satisfaction. On the other end, the solid end, I drill a 1/8" or 3/16" hole through it from side to side. That is for running a throng, or cord through to tie it to my shot pouch. Nothing to it.
Re-enacting, also sometimes called experimental archeology, is going out and actually using the implements, equipment, and known methods of those pioneer people who came before us. When you use these things in real outdoors settings you soon learn what really works and what doesn't.
For instance, a shot bag hanging low on your hip becomes quite a nuisance when you're crawling through the underbrush or running for your life away from some danger. Thus, people learned to keep it short, so it can be clamped against your body with your elbow and won't swing or flap around with every move you make.