In a small saucepan, simmer the pomegranate juice, orange peel, and sugar, stirring frequently, until the liquid thickens and reduces by about half, about 8-10 minutes. The syrup is done when it's the consistency of honey. Move the pot off the heat and let cool.
In your favorite cocktail glass, vigorously stir together 1/2 oz of the pomegranate syrup, the bourbon, apple cider, cranberry juice, and bitters. Add ice and top with ginger beer. Garnish with apple slices, as desired.