Dropping the trinket on the ground does not remove the die until Isaac leaves the room.
Be cautious when carrying cards and/or pills; the die given by Dice Bag will always be first in the consumable queue if it gives one; one unaware press of the "use consumable" button can lead to Isaac's build getting fully rerolled.
Glowing Hour Glass: The die given in the room Isaac used Glowing Hour Glass in will be granted in the next new room Isaac visits, regardless of what it is.
Jacob and Esau: Regardless of who is holding the die, it is activated by pressing the consumable key. If Esau is holding an active item, it will be used at the same time as the die. Possibly unintended behavior.
When Dice Bag gives Isaac a die, it can actually be seen in the list of items in the Pause menu, meaning that Dice Bag grants items, not consumables.
This trinket resembles a bag from Crown Royal, a popular brand of liquor that comes in a purple sack. In real life, these bags are commonly used as dice bags due to their availability.
This item is most likely based on Dice Bag item from Fiend Folio mod. It would give Isaac a Glass Dice every 8 rooms, a single-use consumable that gives Isaac an effect of a dice item.