Multiphase computational fluid dynamics (MCFD) is a promising tool to predict fully turbulent gas-liquid two-phase flows with high resolution. As a complex model, extensive validation and uncertainty quantification are required for an M-CFD solver before it can be trusted for large-scale industrial applications. In this paper, the inverse uncertainty quantification based on Bayesian inference is performed to quantify the uncertainty of the turbulence model in STAR-CCM+. As an inverse approach, the Bayesian approach requires experimental measurements to conduct the inference. In this work, high-resolution turbulence data measured by particle image velocimetry are used. The turbulence model with standard wall function and bubble-induced turbulence is considered. Supported by the PIV data, the uncertainties of the coefficients in the model are quantified, based on which the uncertainties of the solver predictions are evaluated. The Bayesian inference is conducted with the Markov Chain Monte Carlo (MCMC) method, based on a surrogate model constructed with Gaussian Process. It is found that the uncertainty of the turbulent kinetic energy is consistent with the measured data. However, it is also found that the liquid velocity is overestimated in the bulk flow region and underestimated in the near wall flow region compared to the measurement data. Such moderate discrepancies between the solver predictions and measurements require a more comprehensive evaluation that takes all relevant closure relations into consideration.