Graphene bilayers in Bernal stacking exhibit a transverse electric (E) field dependent band gap, thanks to the on-site electron energy asymmetry between the two layers, which can be used to increase the channel resistivity, and enable higher on/off ratio devices. Using dual-gated device structure, we investigate the transport characteristics of exfoliated graphene bilayers as a function of carrier density and E-field at temperature from 295 K down to 0.3 K. At high E-field, strong conduction suppression near the charge neutrality point is observed, a primary characteristic introduced by band gap opening. The conductivity suppression persists up to the finite threshold voltages, which increase with increasing the E-field, similar to a gapped semiconductor. We extract the transport gap as a function of E-field from the threshold measurement, and further discuss the impact of disorder. At gate bias higher than the threshold, conductivity increases linearly as carrier density increases, which contrasts to the sub-linear dependence in graphene monolayer. Mobility shows decreasing tendency with the increasing E-field, which changes little as temperature changes. Besides, we probe the electrical characteristics of quasi-free-standing graphene bilayers grown on SiC at temperature down to 0.3 K, based on the study on the exfoliated graphene bilayers. The epitaxial graphene bilayer on SiC is prepared by atmospheric pressure graphitization in Ar, followed by H₂ intercalation, which renders the material quasi-free-standing. At the charge neutrality point, the longitudinal resistance shows an insulating behavior, and follows a temperature dependence consistent with variable range hopping transport in a gapped state. Besides, clear linear dependence of the conductivity on the carrier density is observed, which is distinguishable from the sub-linear dependence in graphene monolayer. These properties show that the epitaxial graphene bilayer grown on the SiC exhibits band-gap opening and Bernal stacked arrangement. / text