  We analyse the kinematics of the Galactic bar-bulge using proper motions from
the ESO public survey Vista Variables in the Via Lactea (VVV) and the second
Gaia data release. Gaia has provided some of the first absolute proper motions
within the bulge and the near-infrared VVV multi-epoch catalogue complements
Gaia in highly-extincted low-latitude regions. We discuss the
relative-to-absolute calibration of the VVV proper motions using Gaia. Along
lines of sight spanning $-10<\ell/\,\mathrm{deg}<10$ and
$-10<b/\,\mathrm{deg}<5$, we probabilistically model the density and velocity
distributions as a function of distance of $\sim45$ million stars. The
transverse velocities confirm the rotation signature of the bar seen in
spectroscopic surveys. The differential rotation between the double peaks of
the magnitude distribution confirms the X-shaped nature of the bar-bulge. Both
transverse velocity components increase smoothly along the near-side of the bar
towards the Galactic centre, peak at the Galactic centre and decline on the
far-side. The anisotropy is $\sigma_\ell/\sigma_b\approx1.1-1.3$ within the
bulk of the bar, reducing to $0.9-1.1$ when rotational broadening is accounted
for, and exhibits a clear X-shaped signature. The vertex deviation in $\ell$
and $b$ is significant $|\rho_{\ell b}|\lesssim0.2$, greater on the near-side
of the bar and produces a quadrupole signature across the bulge indicating
approximate radial alignment. We have re-constructed the 3D kinematics from the
assumption of triaxiality, finding good agreement with spectroscopic survey
results. In the co-rotating frame, we find evidence of bar-supporting x1 orbits
and tangential bias in the in-plane dispersion field.
