Add the watermelon cubes to a blender or food processor and blend until pureed.
Strain the watermelon puree by pouring it through a mesh sieve to make watermelon juice, pressing it with the back of a spoon to get all the juice through.
Measure out ⅔ cup of watermelon juice for the ice cubes and 3 tablespoons for the watermelon simple syrup.
Make the ice cubes by combining the ⅔ cup of watermelon juice with 1 tablespoon of water. Stir well to mix.
Pour the mixture into an ice cube tray and freeze for 3 to 4 hours to make about half a tray of watermelon ice cubes.
Make the syrup by adding 3 tablespoons of water and the sugar to a small saucepan on medium.
Cook, stirring occasionally, until the sugar is completely dissolved. Remove from the heat and set aside to cool completely.
Pour the reserved 3 tablespoons of watermelon juice into the cooled simple syrup. Stir well to mix and set aside.
When ready to assemble the drinks, pour the watermelon syrup, bourbon, and bitters into a mixing glass filled with ice and stir until well chilled.
Place 3 or 4 watermelon ice cubes each into 2 rocks glasses and strain the mixed liquid into the glasses.
Garnish each glass with a small triangular slice of watermelon and serve immediately.