I washed out some small (8-oz) sized plastic wine bottles with screw-on caps. Poke the snake into the bottle, tail first. Keeps it clean and ready to use.
Also fun making sure I have a sufficient supply of boresnake containers!
Mine all hang on hooks on the pegboard in my shop. If on the off chance I decide to toss one in the range bag for field expedient cleaning then I just coil it up and wrap the cord around the mop portion and toss it in the bag/box.