Magnetosheath jets are localized fast flows with enhanced dynamic pressure. When they supermagnetosonically compress the ambient magnetosheath plasma, a bow wave or shock can form ahead of them. Such a bow wave was recently observed to accelerate ions and possibly electrons. The ion acceleration process was previously analyzed, but the electron acceleration process remains largely unexplored. Here we use multi‐point observations by Time History of Events and Macroscale during Substorms from three events to determine whether and how magnetosheath jet‐driven bow waves can accelerate electrons. We show that when suprathermal electrons in the ambient magnetosheath convect towards a bow wave, some electrons are shock‐drift accelerated and reflected towards the ambient magnetosheath and others continue moving downstream of the bow wave resulting in bi‐directional motion. Our study indicates that magnetosheath jet‐driven bow waves can result in additional energization of suprathermal electrons in the magnetosheath. It implies that magnetosheath jets can increase the efficiency of electron acceleration at planetary bow shocks or other similar astrophysical environments.