Bošković has won seven singles and eight doubles titles on the ITF Circuit.

On the ITF Junior Circuit, she had a career-high combined ranking of 19, achieved on 5 June 2017.

In 2017, she reached the US Open girls' doubles final, partnering Wang Xiyu.

Bošković made her Fed Cup debut for Croatia in 2018, and she has a win–loss record of 6–3.

On her WTA Tour main draw debut, Bošković reached the quarterfinals as a lucky loser at the 2024 Iași Open, defeating Maria Timofeeva and qualifier Varvara Lepchenko, both achieved in straight sets,[3] before losing in the last eight to top seed and eventual champion Mirra Andreeva.