Cooling of hadron beams is critically important in the next generation of hadron storage rings for delivery of unprecedented performance. One such application is the electron-ion collider presently under development in the US. The desire to develop electron coolers for operation at much higher energies than previously achieved necessitates the use of radio-frequency (RF) fields for acceleration as opposed to the conventional, electrostatic approach. While electron cooling is a mature technology at low energy utilizing a DC beam, RF acceleration requires the cooling beam to be bunched, thus extending the parameter space to an unexplored territory. It is important to experimentally demonstrate the feasibility of cooling with electron bunches and further investigate how the relative time structure of the two beams affects the cooling properties; thus, a set of four pulsed-beam cooling experiments was carried out by a collaboration of Jefferson Lab and Institute of Modern Physics (IMP). The experiments have successfully demonstrated cooling with a beam of electron bunches in both the longitudinal and transverse directions for the first time. We have measured the effect of the electron bunch length and longitudinal ion focusing strength on the temporal evolution of the longitudinal and transverse ion beam profile and demonstrate that if the synchronization can be accurately maintained, the dynamics are not adversely affected by the change in time structure.