Bishop Bogović was born into a Croatian Roman Catholic family of father Mijo and mother Manda (née Piršić) near Slunj in the Central Croatia.

After graduation at a primary school in Slunj and a classical gymnasium in the diocesan seminary in Pazin, he was admitted to the Major Seminary here and consequently joined the Theological Faculty at the University of Zagreb, where he studied until 1964,[1] and was ordained as priest on July 5, 1964 for the Diocese of Rijeka–Opatija,[2] after completing his philosophical and theological studies.

Bogović continued his studies at the Pontifical Gregorian University in Rome, Italy from 1966 until 1971 with a Doctor of the Church history degree (thesis La questione della gerarchia ortodossa in Dalmazia nei secoli XVII e XVIII).

After his return from studies in Italy, he performed the following duties: he was the personal assistant of Archbishop Viktor Burić, rector of the Theological Faculty at the University of Rijeka, parish priest in Praputnjak near Bakar, Vicar General of the Archdiocese of Rijeka–Senj and professor of a church history at the University of Rijeka.

On 29 June 1999 he was consecrated as bishop by Archbishop Anton Tamarut and other prelates of the Roman Catholic Church in the St. Vid Cathedral in Rijeka.