At youth level, Bedlow represented Sale Sharks at Under-18, Under-19 and A level and also played for National League 3 North side Rossendale.
Bedlow signed a professional contract with Sale Sharks prior to the 2013–2014 season,[3] where he mostly played for their academy side, the Sale Jets.
He didn't make any appearances for them during the 2013–2014 season, but he did join National League 2 North side Preston Grasshoppers where he made four appearances.[4]
During the 2014–15 season, Bedlow joined National League 1 side Fylde on a dual registration basis[5] and made nine appearances for the side, scoring a try on his debut for Fylde in a 29–29 draw against Darlington Mowden Park.[6] He made his first class debut for Sale Sharks on 1 February 2015 in their 2014–15 LV Cup match against Newcastle Falcons, starting in a 19–39 defeat.[7]
In July 2015, Bedlow had a spell with South African side the Eastern Province Kings, representing their Under-21 side in the 2015 Under-21 Provincial Championship.[8]
On 2 May 2017, it was confirmed that Bedlow signs for Premiership rivals Bristol Bears ahead of the 2017-18 season.[9] He has made 58 first-team appearances during his five seasons with the club.
On 27 February 2023, it was confirmed that Bedlow would return to his old club Sale Sharks on a long-term deal ahead of the 2023-24 season.[10]