Bring the sugar and water to a boil in a small saucepan over medium-high heat. Reduce the heat to medium-low and simmer for 10 minutes.
Add 2 tablespoons of the Grand Mariner and simmer for 5 minutes. Remove from the heat and add the thyme and bitters.
Cool to room temperature, remove the thyme sprig, then add the remaining teaspoon of Grand Marnier. Pour into an airtight container and refrigerate for up to 1 month.