  We investigate transport properties through a rectangular potential barrier
in AB-stacked bilayer graphene (AB-BLG) gapped by dielectric layers. Using the
Dirac-like Hamiltonian with a transfer matrix approach we obtain transmission
and reflection probabilities as well as the associated conductance. For
two-band model and at normal incidence, we find extra resonances appearing in
transmission compared to biased AB-BLG, which are Fabry-P\'erot resonance type.
Now by taking into account the inter-layer bias, we show that both of
transmission and anti-Klein tunneling are diminished. Regarding four band
model, we find that the gap suppresses transmission in an energy range by
showing some behaviors look like "Mexican hats". We examine the total
conductance and show that it is affected by the gap compared to AA-stacked
bilayer graphene. In addition, we find that the suppression in conductance is
more important than that for biased AB-BLG.
