Wash the beets thoroughly, remove the tops and ends, and chop them into small pieces. There is no need to peel them.
Add the chopped beets and water to a blender. Blend until the beets are finely processed.
Strain the mixture through a fine mesh sieve into a large bowl or pitcher, pressing the pulp to extract as much liquid as possible. Discard the pulp.
Pour the strained beet liquid back into the blender. Add the lime juice, whole milk, condensed milk, and Angostura bitters.
Blend until well combined. Taste and add more condensed milk if you prefer a sweeter punch.
Chill well before serving, or serve over ice.