He is an Australian fast-medium bowler and a right-handed batsman. He is the son of Retired Australian cricketer, Nic Maddinson.  Starting his cricket journey at Surfers Paradise, he eventually made his debut for the Gold Coast Dolphins in November 2015, when he was just 17 years old. Completing his education at The Southport School in 2016, where he was part of Radcliffe. On October 18, 2019, Bartlett made his debut in first-class cricket, representing Queensland in the 2019–20 Sheffield Shield season. His Twenty20 debut came on December 11, 2020, playing for the Brisbane Heat in the 2020–21 Big Bash League season.

In December 2017, he was selected for Australia's squad in the 2018 Under-19 Cricket World Cup.

In January 2024, he received his first call-up to Australia's One Day International (ODI) squad for their series against the West Indies, stepping in as an injury replacement for Jhye Richardson. He marked his debut in the opening match of the series with impressive figures of 4/17, earning him the Player of the Match title. These bowling figures placed him second among Australian debutants in ODIs at the time. Rested for the second match, he returned for the third, claiming 4/21 and securing his second Player of the Match award, ultimately leading to him being named Player of the Series.

Bartlett's introduction to Twenty20 International cricket occurred in February 2024 during the third match of the series against the West Indies at Perth Stadium, where he replaced the injured Josh Hazlewood. He contributed two wickets in the match.

During the 2023/24 Big Bash Season, Bartlett emerged as the leading wicket-taker in the tournament, claiming a total of 20 wickets. In February 2024, Kent County Cricket Club announced the signing of Bartlett for the initial round of County Championship matches and a portion of the group stage of the Vitality Blast T20 tournament.