Combine the lime juice, celery seed, and horseradish in a pitcher. Muddle the mixture with the end of a wooden spoon to blend and break up the celery seeds. Pour in the tomato juice, hot sauce, and Worcestershire sauce; season with salt and pepper. Stir everything together to combine.

Divide the vodka among 6 tall, chilled glasses filled with ice. Fill the glasses with the bloody mary mix, stick in the celery and cucumber and garnish with the cilantro. Give the bloody mary a good stir and serve.