The electric field-effect magnetoconductance (EFE-MC) method was applied to study the quantum-size effect in semimetal Bi films. This method uses a magnetic field to adjust the quantum-size characteristics of a semimetal film - in particular, the ratio of the mobilities of the electrons and holes. We present a theoretical analysis of the EFE-MC method and demonstrate its strength experimentally. The characteristic of the quantum-size state of Bi films, namely the ratio of the densities of states of the electron and hole bands, gn/gp, and its relation to the ratio of the hole and electron mobilities, μp/μn, was obtained by determining the crossover magnetic field H0, at which the EFE-MC changes sign. We demonstrate also that the EFE-MC results prove the absence of charge-carrier trapping by showing that all of the extra charge carriers introduced by the EFE contribute to the conductance. The results obtained are in excellent agreement with those obtained in the absence of a magnetic field, and provide an independent confirmation of the latter interpretation.