We present new empirical estimates of the ΔV bump HB parameter for 15 Galactic globular clusters (GGCs) using accurate and homogeneous ground-based optical data. Together with similar evaluations available in the literature, we ended up with a sample of 62 GGCs covering a very broad range in metal content (-2.16 dex <= [M/H] <= -0.58 dex). Adopting the homogeneous metallicity scale provided either by Kraft & Ivans or by Carretta et al., we found that the observed ΔV bump HB parameters are larger than predicted. In the metal-poor regime ([M/H] <~ -1.7, -1.6 dex) 40% of GCs show discrepancies of 2σ (≈0.40 mag) or more. Evolutionary models that account either for α- and CNO-enhancement or for helium enhancement do not alleviate the discrepancy between theory and observations. The outcome is the same if we use the new solar heavy-element mixture. The comparison between α- and CNO-enhanced evolutionary models and observations in the Carretta et al. metallicity scale also indicates that observed ΔV bump HB parameters, in the metal-rich regime ([M/H] >= 0), might be systematically smaller than predicted. Based in part on data obtained from the ESO/ST-ECF Science Archive Facility, from the Isaac Newton Group Archive which is maintained as part of the CASU Astronomical Data Centre at the Institute of Astronomy, Cambridge, and from the Canadian Astronomy Data Centre operated by the National Research Council of Canada with the support of the Canadian Space Agency.