This recipe is for one Bloody Mary; if you're using a mix, use jut the vodka, hot sauce, and garnishes over ice, and none of the other ingredients. To make for a crowd, mix in a large pitcher, increasing the proportions based on the number of guests. Don't include the alcohol in the pitcher for mixing. Serve the pitcher of mixed Bloody Mary alongside glasses filled with ice, garnishes, and the bottle of vodka so guests can measure out their own alcohol; many prefer a lighter drink and want to control how much alcohol goes in.
Pour all ingredients into a cocktail mixer filled with ice and stir for thirty seconds until well mixed. Strain into a tall Collins glass filled with fresh ice.
Skewer a small toothpick (fringe is nice) with the three olives, and another with a couple of lemon (and/or lime) wedges. Place these in the top of the cocktail glass, nestled in the ice. Serve immediately.