In a container, combine all the ingredients except the oysters. Pour into an 8-inch metal baking dish and freeze until ice crystals start to form around the sides, about 30 minutes. Stir with a fork, return to the freezer, and continue to stir with a fork every 45 minutes until uniform ice crystals have formed, about 3 hours.

To serve, spoon 1 1/2 to 2 tablespoons of the frozen bloody mary mixture into the bottom of 6 tall shot glasses and top with an oyster. Top with frozen bloody mary and continue layering for a total of 3 layers of both oysters and bloody mary in each glass.

Serve immediately with cocktail forks.