[7] In 2013, she won a silver medal at the 2013 European Youth Olympic Festival, where she was named the Most Valuable Player and Best Spiker.

[8] In 2014, she led Serbia's U19 national team to a gold medal at the 2014 Women's Junior European Volleyball Championship.

[6] In 2017, Bošković won bronze with the national team at 2017 FIVB Volleyball World Grand Prix, where she was named Best Opposite Player of the tournament.

[16] That same year, Bošković led Serbia to its first-ever title at the 2018 FIVB Volleyball Women's World Championship, where she was once again named Most Valuable Player after amassing a total of 193 points.

[20] At the 2022 FIVB Volleyball Women's World Championship, Serbia defended its title and Bošković was named Most Valuable Player and Best Opposite of the tournament.

[22] At the 2023 Women's European Volleyball Championship, Bošković and the team advanced to the final for the fourth consecutive edition, where they ultimately placed second.

[30][31] Her younger brother, Vuk, is a basketball player and her older sister, Dajana, plays for the Bosnia and Herzegovina women's national volleyball team.

[36] In 2018, Bosnia and Herzegovina's Ministry of Foreign Affairs, Igor Crnadak, presented Bošković with a diplomatic passport.