In a blender container, place watermelon and puree until smooth.
In a small heatproof bowl, use a wooden spoon to mash mint leaves and 1/4 cup of the sugar; add 1/4 cup of the water.
Microwave on high until fragrant, 1 to 2 minutes.
Using a slotted spoon, transfer mint leaves to blender, leaving sugar in bowl.
Blend until mint is chopped.
2. To bowl of sugar mixture, add remaining 1/4 cup sugar and 1/4 cup water.
Microwave until sugar dissolves into a syrup, 1 to 2 minutes.
Cover and chill.
3. To serve, strain watermelon mixture into an iced-filled pitcher or jar; stir in syrup, lime juice, and bitters.
Divide watermelon mixture among ice-filled glasses; top with ginger ale.
Garnish with mint sprigs.
Makes 8 servings.
Make ahead: Cover and chill watermelon mixture up to 8 hours.