We present here a new parameterization for the bulk motions of galaxies and clusters (in the linear regime) that can be measured statistically from the shape and amplitude of the two-dimensional two-point correlation function. We further propose the one-dimensional velocity dispersion (vp) of the bulk flow as a complementary measure of redshift-space distortions, which is model-independent and not dependent on the normalisation method. As a demonstration, we have applied our new methodology to the C4 cluster catalogue constructed from Data Release Three (DR3) of the Sloan Digital Sky Survey. We find vp = 270+433 km/s (also consistent with vp = 0) for this cluster sample (at = 0.1), which is in agreement with that predicted for a WMAP5-normalised ΛCDM model (i.e., vp(ΛCDM) = 203 km/s). This measurement does not lend support to recent claims of excessive bulk motions ( 1000 km/s) which appear in conflict with ΛCDM, although our large statistical error cannot rule them out. From the measured coherent evolution of vp, we develop a technique to re-construct the perturbed potential, as well as estimating the unbiased matter density fluctuations and scale-independent bias.