A Bloody Mary is one of those drinks that are best made organically or in the moment. There is no law governing the perfect Bloody Mary. It's a drink that should be made "in the moment" or as mood and whimsy take you. That's why most bars are extremely disappointing in their Bloody Marys. Most will make up a batch of mix that will sit in the refrigerators for two or three days, and then it's just add vodka and two-day-old vegetables. It may save the bartender time (and the bar money) but you could have asked for a vodka and V-8 juice and spared yourself the wilting celery. Of course, a pre-made mixture probably guarantees you won't get an awful Bloody Mary, but with no risk there's no reward.
In the video below Robert Hess walks you through making a Bloody Mary. Notice, he uses no pre-mix or commercial mixture.
His recipe:
1 1/2oz vodka
3oz tomato juice
1/2 oz lemon juice
celery salt (to taste)
dash Worcestershire sauce
black pepper (to taste)
1 tsp. horseradish
1 tblsp. chili powder