Combine the sugar and water in a small saucepot and bring to a simmer over medium-high heat. Stir until the sugar dissolves. Stir in the ginger, cinnamon sticks, and cloves. Let cool to room temperature, then transfer to a clean container and refrigerate for 2 to 24 hours. Strain out and discard the solids, and return the liquid to the container.
Place the cider in a small saucepot and heat over medium heat until hot. Stir in the bourbon, and 1 tablespoon of the simple syrup, or to taste.
Moisten the rim of each of 4 mugs with a wedge of the lemon. Squeeze the lemon wedge into each of the mugs, and drop the squeezed lemon quarter into each mug. Divide the hot cider drink between the mugs, and serve hot.