Combine tomatoes, celery, jalapeno, and garlic in a blender. Pour in water and blend until very smooth. Pass mixture through a fine-mesh strainer and discard skins.
Add lemon juice, Worcestershire sauce, horseradish, hot sauce, salt, and pepper. Whisk thoroughly; taste and adjust seasonings. Cover Bloody Mary base with plastic wrap and refrigerate until completely chilled, at least 2 hours.
Ladle 1 cup cold Bloody Mary base into each serving bowl. Dollop 2 ounces Burrata cheese into the center. Season with black pepper and drizzle in olive oil.