Everyone seems to think that a dice bag is just a purse. A bag with a string that allows the dice not to fly loose in a backpack.

However, this ordinary object is the basic cover of your beloved sets. It's a cloth armor for all these happy polyhedral dice that help players defeat the dragon, cast a fireball, captivate the evil troll, lull the manticore and resurrect the skeletons' legion to get medieval on their “rear parts”.
Such a dice bag must be durable, nice and suitable for the character's characteristics.