Make the ginger simple syrup: In a small saucepan over medium heat, combine the sugar, water, and ginger. Bring to a low boil, then reduce the heat to low and simmer for 5 minutes, until the sugar is fully dissolved and the ginger is fragrant. Remove from heat and let cool for 5-10 minutes. Strain through a fine-mesh sieve (you should have ⅓ cup (80 ml) syrup).
Fill a 10-cup pitcher halfway with ice. Pour in the ginger simple syrup, orange juice, and prosecco and stir to combine. Top with the bitter orange liqueur and club soda. Fill the pitcher with the orange slices. Serve immediately.