Slice eggs in half lengthwise, and remove yolks. Discard 4 yolks. Chop egg whites and remaining 2 yolks. Add mayonnaise, green olives, mustard, salt, and pepper to eggs. Stir gently.
Spread egg mixture over 4 bread slices; place 2 bacon slice halves and 1/4 cup arugula over egg mixture. Top each with 1 bread slice.