Bazunu started his career at Shamrock Rovers, making his first team debut in June 2018 at the age of 16, before joining Manchester City in February 2019.
[11][12] The following month, it was announced he has signed a pre-contract agreement with Manchester City,[13] with it initially agreed he would join the club in summer 2019, before it was moved forward to February 2019.
[14] Bazunu was named in Manchester City's UEFA Champions League squad for a Round of 16 second leg match against Real Madrid in August 2020.
[15] He signed a contract extension with Manchester City until 2024 and joined League One side Rochdale on a season-long loan later that month.
[26] Ahead of a match against Preston North End on 16 April 2024, he suffered an achilles injury during the warm-up and was expected to miss the remainder of the 2023–24 season.
[30] On 3 February 2025, he joined Belgian Pro League club Standard Liège on loan for the remainder of the 2024–25 season.