Red clump giants in the Galactic bulge are approximate standard candles and hence they can be used as distance indicators. We compute the proper motion dispersions of RCG stars in the Galactic bulge using the proper motion catalogue from the second phase of the Optical Gravitational Microlensing Experiment (OGLE-II, Sumi et al. 2004) for 45 fields. The proper motion dispersions are measured to a few per cent accuracy due to the large number of stars in the fields. The observational sample is comprised of 577736 stars. These observed data are compared to a state-of-the-art particle simulation of the Galactic bulge region. The predictions are in rough agreement with observations, but appear to be too anisotropic in the velocity ellipsoid. We note that there is significant field-to-field variation in the observed proper motion dispersions. This could either be a real feature, or due to some unknown systematic effect.