Using a reamer, juice the blood oranges into a strainer placed over a bowl. With the back of the spoon work the pulp against the strainer to extract all of the juice, about 1/4 cup.
In a small pitcher combine the blood orange juice, lemon juice, bitters, and the chilled cava. Give it a little stir. Pour into a chilled champagne flute. Garnish with a thin slice of blood orange.