  We report the fabrication of electrostatically defined nanostructures in
encapsulated bilayer graphene, with leakage resistances below depletion gates
as high as $R \sim 10~$G$\Omega$. This exceeds previously reported values of $R
=~$10 - 100 k$\Omega$.\cite{Zou2010,Yan2010,Zhu2016a} We attribute this
improvement to the use of a graphite back gate. We realize two split gate
devices which define an electronic channel on the scale of the
Fermi-wavelength. A channel gate covering the gap between the split gates
varies the charge carrier density in the channel. We observe device-dependent
conductance quantization of $\Delta G = 2~e^2/h$ and $\Delta G = 4~e^2/h$. In
quantizing magnetic fields normal to the sample plane, we recover the four-
fold Landau level degeneracy of bilayer graphene. Unexpected mode crossings
appear at the crossover between zero magnetic field and the quantum Hall
regime.
