Career
Sektzia Nes Tziona
Bitton began his career in the youth system of Hapoel Tel Aviv. In August 2010, loaned to Sektzia Nes Tziona, in order to gain playing time. On 7 August 2014 he made his debut in 2–1 victory against Hapoel Bnei Lod at the group stage of the Toto Cup.
Hapoel Nazareth Illit
After his loan period ended, he loaned to Hapoel Nazareth Illit.
He made his debut on 3 September 2012 in a 2–2 draw against Hapoel Ra"anana. On 4 February 2013 he received a red card for a first time at career against Hapoel Rishon LeZion.
Hapoel Be"er Sheva
After his loan period ended, he released from Hapoel Tel Aviv and On 27 June 2013 signed to Hapoel Be"er Sheva, with his teammate Ben Turjeman. On 30 September 2013 he made his debut in the league 1–2 victory against Bnei Yehuda Tel Aviv.
Bitton was part of a successful season for Be"er Sheva, who finished the season in 2nd place.
On 17 July 2014 he made his debut in the European Competition, in the 1–2 loss against RNK Split at Union of European Football Associations Europa League qualifying. On 2 December 2014 he scored his debut career goal at the 1–1 draw against Hapoel Ironi Kiryat Shmona.