Put about 1/4 cup crystallized ginger into your jar.
Pour one (750ml) bottle of bourbon into the container.
Cap the container LOOSELY! The sugars in the ginger can ferment and the gas needs to be able to escape.
Put your mixture in a cool dry place for about a week, tasting to determine if it needs to infuse longer.
Once it's to your liking, place the cheesecloth over the mouth of the jar and pour the infused bourbon into the second clean jar to strain. You may need to strain more than once, but a bit of sediment is fine and not bad.