We propose a method to generate femtosecond, relativistic, and high-charge electron bunches using few-cycle and tightly focused radially polarized laser pulses. In this scheme, the incident laser pulse reflects off an overdense plasma that injects electrons into the reflected pulse. Particle-in-cell simulations show that the plasma injects electrons ideally, resulting in a dramatic increase of charge and energy of the accelerated electron bunch in comparison to previous methods. This method can be used to generate femtosecond pC bunches with energies in the 1–10 MeV range using realistic laser parameters corresponding to current kHz laser systems.