Andria started his youth career in Tbilisi, Georgia at the club Iveria which has become his first junior team. Shortly after winning Georgian championship for several times, he was selected for the junior Georgian national team.
Soon the young talented player continued his career: First in Jadran Herceg Novi where he competed in the senior squad coached by famous Montenegrin water polo player Vladimir Gojković who is currently the coach of the Montenegro men's national water polo team. Second foreign team for the Georgian was CN Barcelona (40 Spanish Championship titles, 19 Spanish League titles), playing División de Honor de Waterpolo, coached by famous Spanish water polo player and coach Toni Esteller.
After clinching the 6th place with CN Barcelona in the national championship, Bitadze continued his career in Rome, becoming the youngest foreign player in Serie A1 for the 2016/2017 season, scoring 9 goals. In the end of the season Roma Vis Nova lost play-out matches and the team was relegated in Serie A2.
For the 2017/2018 season Andria remained in Roma Vis Nova (coach Alessandro Calcaterra) as the only foreign player in the team scoring 18 goals and clinching the 7th place in the championship.
In September 2018 he signed a new contract with a Serbian giant VK Crvena zvezda, the team coached by a legendary player and one of the best coaches in water polo history Dejan Savić, where he was a runner-up of Serbian water polo national championship.
LEN announced a list of clubs which got wild cards for the 2018/19 Champions League Preliminary round. One of the teams is Crvena Zvezda, this will be the debut for the current format of the championship. VK Crvena zvezda won their first and only title in 2012/2013 LEN Champions League season.
After a successful season at VK Crvena zvezda, he returned in Tbilisi to join WPC Dinamo Tbilisi, which for the first time competed in group stage of the LEN Champions League. It was the first time in his career, that he played for a native club on international level. After 3 consecutive seasons, appearing in Champions league together with his hometown club, he continued his foreign journey, by joining Panionios Water Polo Club. With the new club, he managed to reach the semi-finals of the LEN Euro Cup and finishing 4th in the A1 Ethniki Water Polo championship. For the new season, he returned in the Italian Serie A1 (water polo) championship, joining CC Ortigia.
