In a small saucepot, bring 1 cup of water, the maple syrup, ginger, rosemary, cinnamon sticks, and star anise pod to a boil for 5 minutes. Remove from the burner and steep 10 minutes. Strain into a punch bowl or pitcher and discard the solids.
In the bowl or pitcher, stir together the bourbon, syrup, lemon juice, and bitters. Divide into glasses filled with ice and top with the champagne or prosecco. Garnish with rosemary sprigs, cinnamon sticks, and anise pods, as desired.