Bilbija started his career with his hometown club Borac Banja Luka, whose academy he joined in 2000. He made his professional debut on 8 November 2008 against Posušje at the age of 18. He scored his first goal as a professional against Orašje on 7 March 2009. On 29 January 2010 Bilbija moved to Serbian side Vojvodina signing a four-year contract. During his time at the club, he was sent on two loans to his former club, Borac Banja Luka. In August 2013, Bilbija signed a two-year deal with Sarajevo. In July 2015, he joined Split on a two-year contract.
On 11 February 2016, Bilbija signed with Zrinjski Mostar on free transfer. He scored on his competitive debut for the club against his former team Sarajevo on 28 February. In August 2017, Bilbija signed a new two-year deal with Zrinjski Mostar. In a game against Vitez on 26 August, Bilbija scored his first hat-trick for the team. A year later, he scored four goals in a convincing triumph over Zvijezda 09. On 10 November 2018, Bilbija scored a brace on his 100th appearance for the club.
On 23 December 2018, Bilbija joined South Korean side Gangwon for an undisclosed transfer fee. On 4 January 2019, Bilbija officially joined Gangwon after signing a contract with the club. He made his debut for Gangwon on 2 March 2019, in a 2–0 away loss against Sangju Sangmu coming in as a substitute in the 71st minute. Bilbija scored his first goal for Gangwon on 15 May 2019, in a 2–0 home win against Paju Citizenin the round of 16 of the 2019 Korean FA Cup.
Return to Zrinjski Mostar
On 24 December 2019, Bilbija came back to Zrinjski almost a year after joining Gangwon, signing a three and a half year contract which will last until the summer of 2023 with the Mostar based club. In his first game back, Bilbija scored a goal in a 2–0 league win against Čelik Zenica on 23 February 2020.
International career
Bilbija represented Bosnia and Herzegovina at various youth levels. He was the captain of the under-21 side and also top goalscorer in team's history with 9 goals. In August 2017 he received his first senior call-up, for 2018 FIFA World Cup qualifiers against Cyprus and Gibraltar. He debuted in friendly game against United States on 28 January 2018.
