We report on the exchange bias between antiferromagnetic and ferroelectric hexagonal YMnO3 epitaxial thin films sandwiched between a metallic electrode (Pt) and a soft ferromagnetic layer (Py). Anisotropic magnetoresistance measurements are performed to monitor the presence of an exchange bias field. When the heteroestructure is biased by an electric field, it turns out that the exchange bias field is suppressed. We discuss the dependence of the observed effect on the amplitude and polarity of the electric field. Particular attention is devoted to the role of current leakage across the ferroelectric layer. ; Comment: Accepted for publication in Philosophical Magazine Letters (Special issue on multiferroics)