Slice the oranges in half and squeeze them until you've collected 1 1/2 cups (12 ounces) of juice. Strain the juice through a fine mesh sieve into a clean container. Discard any pulp and seeds.
Fill two glasses with ice. Divide the strained orange juice between the two glasses. Add 2 tablespoons of grenadine syrup to each glass (it will naturally sink to the bottom of the glass). Top each glass with 2 ounces of ginger beer and one to two dashes of bitters.
Garnish with orange slices. Stir before serving.
While bitters do technically contain alcohol, they are used at a very small volume in this recipe. It's similar to how we use vanilla extract, which is an alcohol-based flavoring agent, in cakes and cookies.