  We report on a first census of Galactic black hole X-ray binary (BHXRB)
properties with the second data release (DR2) of {\em Gaia}, focusing on
dynamically confirmed and strong candidate black hole transients. DR2 provides
five-parameter astrometric solutions including position, parallax and proper
motion for 11 of a sample of 24 systems. Distance estimates are tested with
parallax inversion as well as Bayesian inference. We derive an empirically
motivated characteristic scale length of $L$=2.17$\pm$0.12 kpc for this BHXRB
population to infer distances based upon an exponentially decreasing space
density prior. Geometric DR2 parallaxes provide new, independent distance
estimates, but the faintness of this population in quiescence results in
relatively large fractional distance uncertainties. Despite this, DR2 estimates
generally agree with literature distances. The most discrepant case is BW Cir,
for which detailed studies of the donor star have suggested a distant location
at >~25 kpc. A large DR2 measured parallax and relatively high proper motion
instead prefer significantly smaller distances, suggesting that the source may
instead be amongst the nearest of XRBs. However, both distances create problems
for interpretation of the source, and follow-up data are required to resolve
its true nature. DR2 also provides a first distance estimate to one source,
MAXI J1820+070, and novel proper motion estimates for 7 sources. Peculiar
velocities relative to Galactic rotation exceed $\sim$ 50 km s$^{-1}$ for the
bulk of the sample, with a median system kinetic energy of peculiar motion of
$\sim$ 5 $\times$ 10$^{47}$ erg. BW Cir could be a new high-velocity BHXRB if
its astrometry is confirmed. A putative anti-correlation between peculiar
velocity and black hole mass is found, as expected in mass-dependent BH kick
formation channels, but this trend remains weak in the DR2 data.
