Born in France to Ivorian parents, Bamba represented Ivory Coast in the 2008 Olympic Games and earned 46 caps for the senior international team between 2008 and 2014.

"[8] After an initial trial period, Bamba signed for Scottish Premier League side Dunfermline Athletic in July 2006 on a two-year contract.

[11] Leishman was immediately impressed by Bamba's physique and his performance as a trialist during a preseason friendly against West Bromwich Albion striker John Hartson.

[19] Soon afterwards, manager Jim McIntyre said he expected a fee to be agreed between Dunfermline and Watford, which would allow Bamba to move to the Championship side.

[20] The deal was thought to be almost complete, with Watford sending a doctor to China, where Bamba had travelled with the Ivory Coast Olympic squad, to conduct his medical.

Despite being a natural centre back, manager Mixu Paatelainen praised Bamba's performance as a defensive midfielder during a 2–0 win over Celtic in December 2008.

[25] Paatelainen commented further that he believed Bamba had improved as a player since his spell at Dunfermline, with him no longer going to ground when making a challenge,[26] and described him as possessing "tremendous pace and physical presence.

[28] In his second match in this position, Bamba scored his first ever professional goal in a 3–1 win against Falkirk on 22 August, heading in from a John Rankin corner.

[30] Sven-Göran Eriksson, the new manager of the Ivorian national team, was also due to watch Bamba ahead of the 2010 World Cup,[30] but was not spotted at the last game played by Hibs in the 2009–10 season.

[35] Bamba was made to train with the club's youth team on his return but was recalled for the second leg of a UEFA Europa League tie with NK Maribor at Easter Road, which Hibs lost 3–2 on the night and 6–2 on aggregate.

[40] He made his debut for the club in a 2–2 draw against Manchester City on 9 January in the third round of the FA Cup, scoring with his first touch of the ball.

[49] He later expressed his regret at leaving the club, stating his belief in Pearson's ability to help them win promotion to the Premier League.

He only made 18 appearances during his first season at the club,[51] missing a proportion of fixtures in December and January in part because he was away with Ivory Coast as they qualified for the 2013 African Cup of Nations.

"[57] On 23 January 2015, less than six months into his Palermo contract,[57] Bamba was loaned to Championship side Leeds United for the remainder of the season, with the possibility of making the transfer permanent at a later date.

[67][68] New Leeds United head coach Uwe Rösler described Bamba as "a match-winner in both boxes", and said that "he brings fantastic qualities with him" and "he can be a leader by himself for the young team he is working with".

On 7 August, Bamba scored an own goal against Queens Park Rangers in a 3–0 defeat in the opening match of the season and was subsequently dropped from the side, falling behind Kyle Bartley, Liam Cooper and Pontus Jansson in the pecking order.

[78] Following his release, Bamba trained with Derby County who were managed by his former Leicester boss Nigel Pearson but was not offered a deal.

[56][4] He made his debut for the club in a Severnside derby match against Bristol City on 14 October, scoring the winning goal as the Bluebirds won 2–1.

After receiving the red card, Bamba clashed with the fourth official before being physically restrained by Warnock and leaving the pitch.

[51] Having missed only one match during the course of the season, he was ruled out for the remainder of the campaign after rupturing his cruciate knee ligaments in a defeat against Wolverhampton Wanderers on 5 March 2019.

[92] He made his return from injury as a substitute on 2 November in a 4–2 home win over Birmingham City and in December he signed a new contract adding one year to his deal.

Bamba won the Sky Bet Man of the Match award for his performance in a 2–0 victory against his former club Cardiff City on 23 October 2021.

[97] On 4 February 2022, Bamba came on as a substitute in the 28th minute of extra time in Middlesbrough's FA Cup tie against Manchester United.

Upon the game going to penalties, he took and converted his team's fifth spot kick and ultimately allowed the Boro to progress to the fifth round of the tournament for the first time since 2015.

[103] Bamba made his competitive debut in a 5–0 win against Malawi in a 2010 FIFA World Cup qualifying match, again as a late substitute.

[103] He played in all of Ivory Coast's matches at the 2010 Africa Cup of Nations, but the team suffered a quarter-final defeat to Algeria after extra time.

[110] Bamba was selected in the Ivory Coast's 23-man World Cup squad,[111] but was dropped from the starting lineup, with midfielder Didier Zokora chosen to partner with Kolo Touré in central defence.

[112] At the 2014 FIFA World Cup, Bamba played in central defence alongside Zokora after Touré contracted malaria before the tournament.

[46] Sven-Göran Eriksson, who managed Bamba at club level for Leicester City and internationally for the Ivory Coast, compared the defender with Franz Beckenbauer.

When it's on, pass it, but if it's not on, just put it up there,"[118] and in December 2017 Warnock branded Bamba and fellow Cardiff centre-half Sean Morrison as better than Virgil van Dijk.