A Wrexham youth team player since the age of 12, Liverpudlian Bickerstaff rose through the ranks before being snapped up by Premier League giants Liverpool.
He returned to the Racecourse after two seasons at Anfield, scoring a flurry of goals at under-18's level and breaking into the first-team.
His debut for the senior side came whilst still on youth terms when he faced Ayr United in the Scottish Challenge Cup, netting a sensational finish.
In the summer of 2020 Bickerstaff signed his professional deal, penning a one-year contract ahead of 2020/21. Bickerstaff made his first league appearance on the opening day of the campaign against Boreham Wood in a 2-1 win.
In February 2021 he joined Caernarfon Town on loan in the Cymru Premier, scoring on his debut after coming off the bench against Aberystwyth.
In March 2021 Bickerstaff signed an extension to his deal until the end of the 2021/22 campaign.