Add several ice cubes to a cocktail shaker, then add in the tomato juice, vodka, lemon juice, horseradish, Worcestershire sauce, pepper, and tabasco sauce. Shake the drink to combine.
Press the lemon wedge around the rim of a 12-ounce (or larger) glass. Pour the celery salt onto a plate and dip the rim of your glass into the celery salt.
Pour the bloody mary into the glass and add your desired garnishes.