In a small saucepan, bring 1 cup water, the sugar and 6 rosemary sprigs to a boil. Lower the heat and simmer until the liquid is clear, about 5 minutes. Let cool; discard the rosemary.
In a pitcher, combine the grapefruit juice, vodka, bitters and 3/4 cup rosemary-sugar syrup. Pour into 6 rocks glasses filled with ice cubes and garnish each with a rosemary sprig.