Place the apple cider, lemon juice, orange juice, orange rounds, thyme sprigs, cinnamon sticks, diced apples, and optional bourbon in a large pitcher.
Stir the mixture carefully until the fruit, herbs, and spices are evenly dispersed throughout the liquid.
Before adding the thyme, gently press or rub the sprigs between your fingers to release more of their natural aroma.
Allow the sangria base to stand at room temperature for 30 minutes, when time permits, so the fruit, thyme, and cinnamon can infuse the cider and citrus juices.
For immediate service, the resting period may be omitted, although the flavors will become more pronounced after the brief infusion.
Just before serving, pour the chilled prosecco into the pitcher.
Stir gently to blend the sparkling wine with the infused cider mixture while preserving as much carbonation as possible.
Divide the sangria among individual glasses, adding a portion of the apples, orange slices, and spices to each serving.