In a glass or pitcher, combine the non-alcoholic ingredients: tomato juice, Tabasco sauce, celery salt, pepper, lemon juice, and Worcestershire sauce. Mix with a spoon.
Some people will put ingredients in a blender or use a cocktail shaker, but these create more work and ultimately lead to an overly foamy drink, which disrupts flavor and texture.
If you don't plan to drink your Bloody Mary right away, place the mixture in the refrigerator. If you'll be drinking it immediately, then you can skip this step.
Once you are ready to drink your cocktail, add two ounces of vodka per glass and mix with a spoon until fully combined. Use a quality vodka with a neutral flavor.
Finally, cool your drink with ice and add your toppings. Celery is traditional, but other options include carrot sticks, blue cheese-stuffed olives, and bacon.