For the pumpkin spice simple syrup: In a large glass container with a tight fitting lid, combine the sugar, pumpkin pie spice and 1 cup warm water. Cover and shake vigorously until the sugar dissolves. Store in the refrigerator for up to 1 month.
For the cocktail: In a cocktail shaker filled with ice, combine the bourbon, vermouth, bitters and 1 ounce of the pumpkin spice simple syrup. Cover and shake vigorously. Strain into a coupe glass and garnish with the apple slice.