  We report the experimental observation of Fabry-P\'erot (FP) interference in
the conductance of a gate-defined cavity in a dual-gated bilayer graphene (BLG)
device. The high quality of the BLG flake, combined with the device's
electrical robustness provided by the encapsulation between two hexagonal boron
nitride layers, allows us to observe ballistic phase-coherent transport through
a $1${\mu}m-long cavity. We confirm the origin of the observed interference
pattern by comparing to tight-binding calculations accounting for the
gate-tunable bandgap. The good agreement between experiment and theory, free of
tuning parameters, further verifies that a gap opens in our device. The gap is
shown to destroy the perfect reflection for electrons traversing the barrier
with normal incidence (anti-Klein tunneling). The broken anti-Klein tunneling
implies that the Berry phase, which is found to vary with the gate voltages, is
always involved in the FP oscillations regardless of the magnetic field, in
sharp contrast with single-layer graphene.
