Place 1-2 blood orange slices and a sprig of thyme into a glass. Use a muddler to gently crush the orange slices and thyme.
Fill the glass halfway with ice. Pour the vodka, blood orange juice, and simple syrup over the ice and then fill the glass with ginger beer. Gently stir to combine.
Top with a dash of orange bitters if desired and garnish with more blood orange slices and fresh thyme.