We study both numerically and experimentally the breakup of a viscoelastic liquid bridge formed between two parallel electrodes. The polymer solutions and applied voltages are those commonly used in electrospinning and near-field electrospinning. We solve the leaky-dielectric finitely extensible nonlinear elastic-Peterlin (FENE-P) model to describe the dynamical response of the liquid bridge under isothermal conditions. The results show that the surface charge screens the inner electric field perpendicular to the free surface over the entire dynamical process. The liquid bridge deformation produces a normal electric field on the outer side of the free surface that is commensurate with the axial one. The surface conduction does not significantly affect the current intensity in the time interval analyzed in the experiments. The force due to the shear electric stress becomes comparable to both the viscoelastic and surface tension forces in the last stage of the filament. However, it does not alter the elastocapillary balance in the filament. As a consequence, the extensional relaxation times measured from the filament exponential thinning approximately coincides with the stress relaxation time prescribed in the FENE-P model. The above results allow us to interpret correctly the experiments. In the experiments, we measure the filament electrical conductivity and extensional relaxation time for polyethylene oxide (PEO) dissolved in deionized water and in a mixture of water and glycerine. We compare the filament electrical conductivity with the value measured in hydrostatic conditions for the same estimated temperature. Good agreement was found for PEO dissolved in water + glycerine, which indicates that the change in the filament microscopic structure due to the presence of stretched polymeric chains does not significantly alter the ion mobility in the stretching direction. Significant deviations are found for PEO dissolved in deionized water. These deviations may be attributed to the heat transferred to the ambient, which is neglected in the calculation of the filament temperature. We measure the extensional relaxation time from the images acquired during the filament thinning. The relaxation times obtained in the first stage of the exponential thinning hardly depend on the applied voltage. Little but measurable influence of the applied voltage is found in the last phase of the filament thinning.