In a small saucepan, simmer the balsamic vinegar over medium-low heat until it has reduced to 1/4 cup, about 5 minutes
In a large pitcher, combine 2 tablespoons of the reduced balsamic vinegar, tomato juice, lime juice, horseradish, Worcestershire sauce, celery salt, and hot sauce.
Place the chopped celery stalks in a food processor and pulse until coarsely ground. Add about 1 cup of the tomato mixture and process until pureed. Pour the celery mixture back into the pitcher with the rest of the tomato juice mixture.
To make each drink, fill a glass with ice. Add 1/4 cup of vodka and top with the bloody mary mix. Drizzle with a little of the remaining balsamic vinegar. Garnish with a lime wedge, celery stalk, and olives.