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.