In a blender or food processor, puree together the blueberries and sugar until smooth.

Using a fine-mesh sieve set over a large bowl, pour the blueberry mixture over the sieve. Press the puree into the sieve to extract as much liquid as possible. Discard the solids. Stir in the remaining ingredients.

Pour mixture into an ice cream maker and churn according to manufacturer's instructions. Meanwhile, place an airtight container in the refrigerator while churning the sherbet. (Keeping your container cold will help the ice cream freeze quicker when stored.)

Transfer sherbet to chilled container and place in the freezer to harden at least 2 hours or overnight. Store up to 2 weeks in the freezer.