Kammala jumla mai zuwa: John XXIII ya sanya shi Cardinal-Deacon na "Sant'Eugenio" a cikin taron na 28 Maris 1960. Daga baya aka nada Cardinal Bacci a matsayin babban bishop na "Colonia a Cappadocia" a ranar 5 ga Afrilu, 1962, kuma ya karɓi keɓewarsa na bishop a ranar 19 ga Afrilu daga John XXIII, tare da Cardinals Giuseppe Pizzardo da Benedetto Aloisi Masella suna aiki a matsayin co-consecrators. Ya halarci Majalisar Vatican ta biyu daga 1962 zuwa 1965, kuma ya shiga cikin
Taro na shekara ta 1963 wanda ya zaɓi Paparoma Paul VI.