Place 1 cup water and 3 cups of the Bloody Mary mix in a large saucepan; bring to a boil over high.
Remove from heat. Add shrimp; cover and let stand until shrimp are barely opaque in centers, about 8 minutes.
Immediately stir ice into shrimp mixture to stop cooking; let stand until shrimp are cool, about 5 minutes. Drain shrimp, and pat dry.
Prepare Marinade
Stir together cocktail sauce, vodka, oil, lemon juice, hot sauce, Worcestershire, celery seeds, pepper, and remaining 1 cup Bloody Mary mix in a large bowl or a large heavy-duty ziplock plastic freezer bag.
Stir shrimp, sliced celery, and onion into cocktail sauce mixture. Cover (or seal bag), and place in refrigerator to marinate at least 8 hours or, preferably, up to 24 hours.
Transfer shrimp mixture to a large serving bowl. Top with desired garnishes, and serve immediately.
Notes
The dish can be made in advance. Store, covered, in refrigerator up to 3 days.