Bamba began his career at Paris Saint-Germain, progressing through their youth system before featuring for their reserve team. In 2006, he moved to Scotland, joining Dunfermline Athletic, where he quickly became known for his powerful and commanding defensive presence. His strong performances led to a move to Hibernian in 2008.
In January 2011, Bamba joined Leicester City in England, making a significant impact during his time there. He subsequently had spells with Turkish club Trabzonspor and Italian side Palermo, before returning to England to play for Leeds United, where he also served as club captain.
His most notable period was arguably with Cardiff City, whom he joined in 2016. He quickly became a fan favourite and a pivotal player, helping the club secure promotion to the Premier League during the 2017–18 season. After leaving Cardiff, he concluded his playing career with Middlesbrough.
Internationally, Bamba earned his first cap for Ivory Coast in 2008. He represented his country at two FIFA World Cups (2010 and 2014) and multiple Africa Cup of Nations tournaments. He was part of the Ivory Coast squad that won the 2015 Africa Cup of Nations.
Following his retirement from playing, Bamba transitioned into a coaching career. He has held various coaching roles, including as a first-team coach at Middlesbrough. He is widely recognized for his leadership qualities, physical playing style, and passionate commitment on the field.