The time evolution of the positive ion energy distribution functions (IEDF's) at the substrate position in an asymmetric bipolar high-power impulse magnetron (HiPIMS) system was determined using a gridded energy analyser. This was done for a range of operating conditions, namely the positive voltage Urev and “on-time” negative pulse duration τneg. The magnetron was equipped with a Nb target. Based on the knowledge of the IEDF's, the bombarding ion flux density Γi and energy flux density Qi to a grounded surface were calculated. Time-resolved IEDF measurements showed that ions with energies approaching the equivalent of the positive pulse voltage Urev were generated as the reverse positive voltage phase developed. On time-average, we observed that increasing the set Urev value (from 0 to 100 V), resulted in a marginal decrease in the ion flux density Γi to the analyser. However, this is accompanied by a 5-fold increase in the ion energy flux density Qi compared to the unipolar, Urev = 0 V case. Reducing the negative HiPIMS pulse duration τneg (from 130 to 40 µs) at a constant discharge power leads to a modest increase in Γi, but a 4-fold increase in Qi. The results reveal the benefit of the bipolar HiPIMS technique, in which it is possible to control and enhance the power density of ions bombarding a grounded (or fixed bias) substrate, for potentially better tailoring of thin film properties.