Combine tomato juice, vodka, lemon juice, Worcestershire sauce, salt, pepper, and hot sauce; stir well. Chill thoroughly.
Place 1/4 cup lemon or lime juice in a saucer. Place coarse salt in another saucer. Spin rim of each glass in juice and then in salt. Carefully place ice cubes in glass; pour Bloody Mary mixture over ice. Garnish each serving with a lime slice.