After weeks of speculation, Norwich City confirmed the signing of 18 year old right back Bali Mumba from Sunderland on 27th July 2020. He signed a four year deal. It is reported that Norwich paid £500,000 for the signature of the England youth international who has played for his nation at every level from under-16s to under-19s.

Mumba made his senior debut for Sunderland against Wolverhampton Wanderers on the last day of the 2017–18 EFL Championship season, coming on as an 87th-minute substitute for captain John O'Shea, who handed him the captain's armband as he entered the field of play.

Mumba spent the second half of 2019/20 on loan with non-league outfit South Shields and leaves Sunderland having made only 10 appearances for the club.

He is expected to join the Norwich first team squad.

After a strong pre-season Mumba made his competitive first team debut for Norwich in the Carabao (League) Cup first round clash at Luton on 5th September 2020 which Norwich lost 3-1. The Canaries had 15 first teamers missing due to international call-ups with a further two injured. He made a further five appearances during 2020/21 as the Canaries won the Championship title.

On 6th January 2022, Bali joined Peterborough until the end of the 2021/22 season. He had made just three appearances and as Dean Smith said “With Sam Byram coming back from injury and Max Aarons in front of him, his chances of playing first team football are going to be minimal at the moment, given the quality of the players in front of him.” Posh boss Darren Ferguson said “I am very happy to get Bali signed. He is comfortable at both left and right-back and can also play as a wing-back. He will be an important addition to the squad, and I am really looking forward to working with him for the rest of the season."

Bali scored the winning goal on his Posh debut, a 2-1 defeat of Bristol Rovers in the FA Cup on 8th January 2022. He made 13 appearances for Peterborough who were relegated to League One on 23rd April 2022.

On 7th July 2022, transfer expert Pete O'Rourke reported that Mumba was going to join League One side Plymouth Argyle on a season-long loan. This became reality on 14th July with Argyle boss Steven Schumacher stating ""Bali Mumba will add pace, directness and excitement to our right wing-back department this season. The physical demands required in that area of the pitch for us is immense, so having real competition now on both sides will improve our chances."

He won the League One Young Player of the Month for September 2022 after his positive start at Plymouth, scoring twice and providing two assists in 12 games, all of which he started. Mumba helped Plymouth win promotion to the Championship when they beat Burton Albion 1-0 on 29th April 2023. He had been named EFL League One Young Player of the Year on 23rd April 2023. He said "It's been an amazing experience for me. It's still not done and we've still got a little bit more to push but I want to say a huge thank you to the gaffer (Steven Schmaucher), the staff, my teammates and Plymouth Argyle Football Club for the opportunity and the platform and opportunity to play," Plymouth secured the League One title on 7th May 2023 with a 3-1 win at Port Vale.

Mumba returned to Plymouth on 21st July 2023 for a record-equalling club fee believed to be £1million. He signed a four year deal. "Bali's pace, directness and positivity were huge parts of our success last season, and I know he was someone that the Green Army found tremendously exciting to watch," said Argyle manager Steven Schumacher. The form in pre-season of Kellen Fisher is believed to have influenced Norwich's decision to cash in on Mumba.