Mix together mayonnaise, ketchup, horseradish, juice, pepper sauce and salt in bowl. Add scallion and parsley. Cover; refrigerate at least 1 hour or up to 2 days.
Bring 3 quarts of water to boil. Add shrimp, salt and bay leaf. Boil 1 to 2 minutes, until pink and cooked through. Drain in colander; run under cold water to stop cooking. Drain; place in bowl. Cover; refrigerate until ready to serve with sauce.