Place the apple cider, peppercorns, one of the cinnamon sticks, the cloves, and the star anise in a medium saucepan. Cut a large (1 by 4-inch) peel from the orange using a vegetable peeler and add it to the pan. Bring the cider mixture to a boil, lower the heat, and simmer for 5 minutes. Strain into a 4-cup glass measuring cup and discard the solids.
Pour the hot cider into mugs or heatproof glasses. Add 2 tablespoons of bourbon to each mug. Cut the orange in half through the stem, slice crosswise in 1/4-inch-thick half-rounds, and add one slice to each mug. Cut the apple in half through the stem, remove the core, slice crosswise in 1/4-inch-thick half-rounds, and add one slice to each glass.
Serve hot with a cinnamon stick in each glass for stirring.