Combine the grape juice, rosemary and ginger in a 2-quart saucepan. Reduce the mixture for 1 hour over medium-low heat. When the mixture has reduced by half, add the balsamic and continue cooking until the mixture has reduced by half again, about 10 minutes. Cool for 30 minutes. Strain and store in an airtight container in the refrigerator for up to a week.
Add 1 ounce of the grape syrup to each champagne flute. Top with 4 ounces champagne and 2 to 3 dashes of bitters. Top each glass with a skewered grape half and orange rind piece.
