Born in Oumé, Kalou started playing for ASEC Mimosas in his home country, before moving to Dutch-based Feyenoord. He played in Rotterdam for six seasons as a first team regular. He mainly played as a winger, but also played as a striker when necessary. Meanwhile, his brother, Salomon, who came to visit him, impressed the Feyenoord staff and was signed as a youth player. When Bonaventure decided to leave Feyenoord and try his luck in another European competition, the Ligue 1, at AJ Auxerre, Salomon was sent to Feyenoord's partner Excelsioron loan, before taking over his brother's role. Bonaventure played two seasons at Auxerre, where he developed further as a striker and an attacking midfielder as opposed to a winger. However, he still managed to score a similar number of goals compared to previous seasons. It was in this period that he talked to his brother, who still played at Feyenoord, into acquiring Dutch citizenship, which eventually was rejected by Dutch Foreign MinisterRita Verdonk. In 2005–06, he was transferred to Auxerre's Ligue 1 rivals Paris Saint-Germain. Paris Saint-Germain started to become a relegation-threatened team and he soon signed for another French team, RC Lens. The future looked bright for them, but they were surprisingly relegated at the end of the season. Kalou returned to the Netherlands in 2008 with SC Heerenveen, with whom he won the Dutch Cup in 2009. Heerenveen beat FC Twente in the final, and Kalou scored a goal. In the end of 2009, he was on trial at Crystal Palace and Le Mans, but both trials were unsuccessful. In February 2011, Kalou announced his retirement from professional football. He joined French lower league amateur club Combs-la-Ville for the 2011–12 campaign.
His younger brother, Salomon, also played for Feyenoord. In the build-up to the 2006 FIFA World Cup, there was speculation that the brothers could have become the first to play against each other in a World Cup match, as Salomon was attempting to gain fast-track Dutch citizenship. This did not happen and ultimately Salomon would also play for the Ivory Coast, though not until after the World Cup. In October 2018, Kalou has been elected mayor of Vavoua, a city located in central part of the country. He was elected during municipal elections, running as an independent candidate.