Bristrić was born in Tuzla and grew up in Gradačac.[6][7] He began his football career with ŠN Trijumf at the age of 6, before joining the youth ranks of his hometown club Zvijezda Gradačac.[7] He then spent a short time in the academy of the Croatian club Osijek,[8] but due to paperwork problems he could not be signed and registered and therefore returned to Bosnia and Herzegovina in 2020, signing with Zrinjski Mostar.[7] A year later, he switched to Sloboda Tuzla's youth setup, and then returned to Croatia with Rijeka in June 2021.[9]
In early 2022, Rijeka sent him on a six-month loan to Hrvatski Dragovoljac.[10] There, Bristrić made his senior debut in the 1. HNL, making fourteen appearances and scoring his first career goal in a 5–0 triumph over Šibenik on 11 February.[11]
In January 2023, Bristrić moved to Slovenia by committing to Olimpija Ljubljana of the top-tier Slovenian PrvaLiga. The transfer was announced on 15 December 2022 and he signed a contract until June 2026.[12][13] On 22 February 2023, Bristrić scored his first two goals for Olimpija, in a league game against Gorica, which Olimpija won 4–3.[14] Bristrić stood out again on 15 March, during a league match against Celje, scoring the only goal of the game in a 1–0 win.[15] With Olimpija, Bristrić won the Slovenian PrvaLiga title in 2022–23, and contributed four goals in fourteen league appearances.[5][16]
International career
Bristrić has been capped for Bosnia and Herzegovina at all youth levels from under-17 to under-21.[17][18]
