The accuracy of single-electron currents produced in hybrid turnstiles at high operation frequencies is, among other errors, limited by electrons tunneling in the wrong direction. Increasing the barrier transparency between the island and the leads, together with the source-drain bias, helps to suppress these events in a larger frequency range, although they lead to some additional errors. We experimentally demonstrate a driving scheme that suppresses tunneling in the wrong direction, thus extending the range of frequencies for generating accurate single-electron currents. The main feature of this approach is an additional ac signal applied to the bias with frequency twice that applied to the gate electrode. This allows additional modulation of the island chemical potential. By using this approach under certain parameters, we improve the single-electron current accuracy by one order of magnitude. Finally, we show through experimentally contrasted calculations that our method can improve accuracy even in devices for which the usual gate driving gives errors of the order of 10-3 at high frequencies and can bring them under 5×10-4.