On 19 September 2015, Bassett made his Football League debut for Yeovil Town in a 1–0 victory against Crawley Town,[5] at the age of just 17 years, 6 months and 13 days he broke the record for the youngest Yeovil player in the Football League.[6] On 3 December 2015, Bassett was awarded his first professional contract with Yeovil Town, committing him to the club until June 2017.[7]
On 13 September 2016, Bassett joined Southern League Premier Division side Dorchester Town on an initial one-month loan deal.[8] Bassett made his debut the following day as a second-half substitute in Dorchester's 4–0 victory against Frome Town, with Bassett providing the assist for the fourth goal.[9] Having made four appearances in his first loan spell with Dorchester, Bassett returned on loan to the Southern League club on 28 October 2016.[10]
On 3 February 2017, Bassett joined Dorchester for a third loan spell.[11]
At the end of the 2016–17 season, Bassett was released by Yeovil having only made two appearances for the club.[12]
Following a stint with Nuneaton Borough, Bassett signed with Canadian Premier League side Pacific FC on 29 April 2021.[15] In his season with the Tridents, Bassett contributed with 2 goals and 3 assists as Pacific won the league. After a strong start to the season, Bassett started to see his minutes decrease as the season progressed, and did not play a single minute in the playoffs. Despite interest from the club to trigger his club option for next season, Bassett preferred to move on and find an opportunity to play more regular minutes elsewhere.[16] In January 2022, Pacific confirmed that Bassett had left the club.[17]
Atlético Ottawa
In January 2022, Bassett switched to Canadian Premier League side Atlético Ottawa signing a two-year contract with an option for a third year.[18] On Jun 9, 2022, capping off a hot start to the season, Bassett was named the CPL's Player of the Month for the month of May 2022.[19] Bassett played a crucial role for Ottawa, and led to the team to finish as regular season champions, but they ultimately lost in the final to Forge FC. On October 28, 2022, he was awarded the CPL's Player of the Year and Player's Player of the Year awards.[20][21] In 2023, Bassett, along with Cavalry's Myer Bevan, led the league in scoring with 11 goals.[22] After the 2024 season, he announced his departure from the club.[23]
Tampa Bay Rowdies
On 27 November 2024, the Tampa Bay Rowdies announced that they had signed Bassett as their first new player ahead of the 2025 season.[24]