Given a contraint on the total amount of feedback overhead, we investigate the allocation of feedback bits (i.e. codebook sizes) among users in a limited feedback Zero Forcing Beamforming-based MU-MIMO scheme where users have the opportunity to adapt their codebooks as a function of their own channel statistics. We consider both single-polarized and dual- polarized scenarios. Using upper bounds on the total rate loss incurred by quantization (previously derived by the authors), the optimal bit allocation strategy among users is derived as a function of the users channel statistics and SNR. Closed form solutions of the optimal bit allocation at low and high SNR are also derived. It is shown that in single-polarized scenarios (resp. dual-polarized scenarios) at high SNR it is beneficial to allocate more bits to users experiencing rank deficient transmit correlation matrices (resp. low cross-polarization discrimination XPD) than to users experiencing well conditioned correlation matrices (resp. large XPD), while an opposite allocation should be done at low SNR. Simulation results are shown to confirm analytical derivations.