ABSTRACT Galaxy cluster masses, rich with cosmological information, can be estimated from internal dark matter (DM) velocity dispersions, which in turn can be observationally inferred from satellite galaxy velocities. However, galaxies are biased tracers of the DM, and the bias can vary over host halo and galaxy properties as well as time. We precisely calibrate the velocity bias, bv – defined as the ratio of galaxy and DM velocity dispersions – as a function of redshift, host halo mass, and galaxy stellar mass threshold ($M_{\rm ⋆ , sat}$), for massive haloes ($M_{\rm 200c}\gt 10^{13.5} \, {\rm M}_⊙$) from five cosmological simulations: IllustrisTNG, Magneticum, Bahamas + Macsis, The Three Hundred Project, and MultiDark Planck-2. We first compare scaling relations for galaxy and DM velocity dispersion across simulations; the former is estimated using a new ensemble velocity likelihood method that is unbiased for low galaxy counts per halo, while the latter uses a local linear regression. The simulations show consistent trends of bv increasing with M200c and decreasing with redshift and $M_{\rm ⋆ , sat}$. The ensemble-estimated theoretical uncertainty in bv is 2–3 per cent, but becomes percent-level when considering only the three highest resolution simulations. We update the mass–richness normalization for an SDSS redMaPPer cluster sample, and find our improved bv estimates reduce the normalization uncertainty from 22 to 8 per cent, demonstrating that dynamical mass estimation is competitive with weak lensing mass estimation. We discuss necessary steps for further improving this precision. Our estimates for $b_v(M_{\rm 200c}, M_{\rm ⋆ , sat}, z)$ are made publicly available.