[6][7] Bitton broke into the senior team of his home-town club SC Ashdod at the age of 17 in an Israeli Premier League match on 25 April 2009, and went on to make over 120 appearances.

[9] He made his debut for the club on 18 September, in a Champions League group stage match against AC Milan, coming into the game as a late substitute in the 89th minute.

[10][11] Three weeks later he made another Champions League appearance for Celtic, coming as a 77th-minute substitute against Ajax on 22 October, but was sent off eleven minutes later for a late tackle on Thulani Serero.

[10] The resulting suspension and a few niggling injuries hindered Bitton's efforts to establish himself in the team,[12] but he still managed to make a total of 20 appearances for Celtic by the end of his first season there.

[18] To begin the 2015–16 season, on 19 August 2015, Bitton scored against Swedish side Malmö FF in a 3–2 win at Celtic Park in the first leg of the Champions League playoffs.

[26][27][28] On 1 July 2022, Bitton joined Israeli Premier League club Maccabi Tel Aviv on a free transfer, signing a two-year contract with an option for a third year.