On 24 September 1731, Bijanković was appointed the bishop of Makarska. He was consecrated in Venice on 10 February 1732, with Marco Gradenigo, the patriarch of Venice as the principal consecrator and Nikola Tomašić, the bishop of Skradin and Pietro Maria Suárez, the bishop of Feltre as the co-consecrators.
Bijanković arrived in Makarska at the beginning of the summer of that year. Blašković sent thirteen reports to the Congregation for the Propagation of the Faith about his pastoral visits from 1734 to 1771. In 1756, he finished constructing the Makarska Cathedral. He built the Church of St. Philip Neri in 1757 and a building for the Oratorians (which burnt down on 20 September 1766). In 1772, Blašković also built a lodging with special rooms for Illyrian clergy, including those being educated in Makarska.
Based on the traditional right as the bishop of Makarska, Blašković also administered the Diocese of Duvno under the Ottoman occupation, which he visited during Jul and August 1735. In his report from 25 May 1734 to the Holy See, Blašković states that parts of the diocese were under the care of the Franciscans of the Fojnica friary. During his visit, Blašković stayed in Studenci, Gradac, Vir, Zavelim, Roško Polje, Buško Blato and the Duvanjsko Polje, where he stayed for around ten days. While in the Duvanjsko Polje, Blašković met with the Muslim beys of the Kopčić family, who were present during the Catholic ceremonies and asked him for prayers and relics. Then, Blašković went to Rama where he also stayed for around ten days and met with the local Muslim beys and the kadi of Prozor. The beys blamed him for the flight of the Catholics in 1687 and accused the Franciscans of destroying the Rama friary. To prevent further exodus of the Catholic serfs and return those who fled, the beys asked Blašković to reside in Rama, promising him the Franciscan possessions and a pay of 300 sequins and additional means for maintenance. Blašković went on to visit Rakitno and then Mostar. Blašković visited Rama again in 1737.
Following the Treaty of Passarowitz, Pope Clement XII established the Apostolic Vicariate of Bosnia, which incorporated the dioceses and the parts of the dioceses under Ottoman occupation. These included the Diocese of Duvno and Bosnia and the parts of the Diocese of Makarska and the Archdiocese of Split. Thus, the church aligned its organisation to the political situation. The initiative came from the Bosnian Franciscans led by Archbishop Vicko Zmajević of Zadar. It was in line with the Ottoman policy that the Catholic clergy and bishops should be Ottoman subjects. The Congregation accepted this initiative and on 20 June 1735, asked the pope to appoint a special bishop for the Catholics under the Ottoman occupation, and that he should be from the ranks of the Bosnian Franciscans. To keep the parishes incorporated to the vicariate, Blašković continued to make pastoral visits to them and establish new parishes by dividing the larger ones. For this reason, he came into conflict with the Bosnian Franciscans. In his report to the Holy See from 7 November 1749, he mentioned specific areas of the dioceses regarding which he was in dispute with the bishop of Bosnia.
Blašković published the translation of Robert Bellarmine's catechism under the title Nauk kršćanski (The Christian teaching) in Venice in 1758.
Blašković died in Makarska and is buried in the Church of St. Philip.