  Ongoing experimental progress in the preparation of ultra-clean
graphene/superconductor (SC) interfaces enabled the recent observation of
specular interband Andreev reflections (AR) at bilayer graphene
(BLG)/NbSe$_{2}$ van der Waals interfaces [Nature Physics 12, (2016)].
Motivated by this experiment we theoretically study the differential
conductance across a BLG/SC interface at the continuous transition from high to
ultra-low Fermi energies $E_{F}$ in BLG. Using the Bogoliubov-deGennes
equations and the Blonder-Tinkham-Klapwijk formalism we derive analytical
expressions for the differential conductance across the BLG/SC interface. We
find a characteristic signature of the cross-over from intra-band retro- (high
$E_{F}$) to inter-band specular (low $E_{F}$) ARs, that manifests itself in a
strongly suppressed interfacial conductance when the excitation energy
$|\varepsilon |=|E_{F}|<\Delta $ (the SC gap). The sharpness of these
conductance dips is strongly dependent on the size of the potential step at the
BLG/SC interface $U_{0}$.
