Stir together 1/3 cup mayonnaise and next 7 ingredients.
Spread remaining 1/3 cup mayonnaise evenly over 1 side of each bread slice. Spread 4 bread slices, mayonnaise side up, evenly with half of egg salad. Top evenly with half of spinach and 4 bread slices.
Repeat procedure with remaining egg salad, spinach, and bread slices. Cut each sandwich into quarters; garnish, if desired.
Sweet-Pickle Egg Salad Club: Omit bacon and chives. Add 2 tablespoons instant potato flakes and 1 tablespoon sweet pickle relish; proceed with recipe as directed.
Shrimp-Egg Salad Club: Omit bacon. Add 2/3 cup finely chopped boiled shrimp, 1/2 teaspoon grated lemon rind, and 1/4 teaspoon ground red pepper. Proceed with recipe as directed.