Place tomato juice in a large container with a tight-fitting lid. Add lemon juice, Worcestershire sauce, horseradish, garlic, pepper, and Tabasco; shake vigorously. Taste, and adjust for seasoning; the mixture should be quite spicy.
Pour 1 part vodka and 3 parts Bloody Mary mix over ice in a shaker. Shake well. Pour into glasses. Squeeze a wedge of lemon over drink (do not subsequently stir or shake drink), discard used wedge. Garnish with a large stick of celery (reserve extra stalks for munching) and a large lemon wedge.