Wash the star fruits thoroughly, then cut them into pieces small enough to fit into your blender. There is no need to trim the ridges or remove the seeds.
Add the chopped star fruit to a blender with 2 cups of water. Blend until the fruit is broken down as finely as your blender allows.
Pour the blended mixture through a fine-mesh strainer into a pitcher or bowl, pressing gently to extract the juice. Discard the remaining pulp.
Add the lime juice, sugar, and bitters to the strained juice. Stir until the sugar dissolves.
Taste and adjust the sweetness as needed. If the juice is too tart or concentrated, add a little more water until it reaches your preferred taste.
Refrigerate until chilled, then stir and serve over ice.