The use of microbial gas fermentation for transforming captured CO2 into sustainable fuels and chemicals has been identified as a promising decarbonization pathway. To accelerate the scale-up of gaseous CO2 fermentation reactors, computational models need to predict gas-to-liquid mass transfer which requires capturing the bubble size dynamics, i.e. bubble breakup and coalescence. In this work, an inverse modeling approach is used to calibrate the breakup and coalescence closure models, that are used in the Multiple-Size-Group (MUSIG) population balance modeling (PBM). The calibration aims at replicating experimental results obtained in a CO2-air-water-coflowing bubble column reactor. Bayesian inference is used to account for noise in the experimental dataset and bias in the simulation results. The estimated simulation bias also allows identifying the best-performing closure models irrespective of the model parameters used. The calibration results suggest that the breakage rate is underestimated by one order of magnitude in two different breakup modeling approaches.