Jazzi Barnum-Bobb began his career in the youth team at Watford but would be released in 2014 without making a senior appearance. That summer he made his way to Wales for the first time signing a one-year junior contract with Cardiff City under Ole Gunnar Solsjkaer.
He made his senior debut in professional football in August 2014 for the Bluebirds in the EFL Cup, playing 66 minutes in a 2-1 win against Coventry City.
He made a further appearance that month against in the EFL Cup, in a 2-3 win over Port Vale.
In October 2015 he joined Newport County on loan in Sky Bet League Two making his debut in a 1-0 loss to Portsmouth at Rodney Parade. He went on to total 14 appearances for the Exiles during his temporary switch.
In the summer of 2016 he signed for Newport permanently, scoring his first senior goal against Accrington Stanley in October 2016. Having made over 50 appearances for County he moved out on loan to Torquay United in 2017.
In February 2018 he left Newport due to personal reasons and signed for Chelmsford City to maintain his fitness. After over 12-months with the National League South side he departed and arrived in Wales for a third time, on trial with the Dragons.
After a handful of pre-season appearances, he was snapped up on a one-year deal and made his debut in August 2019 in a 1-0 home win over FC Halifax Town.