When a magnetosheath jet (localized dynamic pressure enhancements) compresses ambient magnetosheath at a (relative) speed faster than the local magnetosonic speed, a bow wave or shock can form ahead of the jet. Such bow waves or shocks were recently observed to accelerate particles, thus contributing to magnetosheath heating and particle acceleration in the extended environment of Earth’s bow shock. To further understand the characteristics of jet‐driven bow waves, we perform a statistical study to examine which solar wind conditions favor their formation and whether it is common for them to accelerate particles. We identified 364 out of 2859 (~13%) magnetosheath jets to have a bow wave or shock ahead of them with Mach number typically larger than 1.1. We show that large solar wind plasma beta, weak interplanetary magnetic field (IMF) strength, large solar wind Alfvén Mach number, and strong solar wind dynamic pressure present favorable conditions for their formation. We also show that magnetosheath jets with bow waves or shocks are more frequently associated with higher maximum ion and electron energies than those without them, confirming that it is common for these structures to accelerate particles. In particular, magnetosheath jets with bow waves have electron energy flux enhanced on average by a factor of 2 compared to both those without bow waves and the ambient magnetosheath. Our study implies that magnetosheath jets can contribute to shock acceleration of particles especially for high Mach number shocks. Therefore, shock models should be generalized to include magnetosheath jets and concomitant particle acceleration.