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.
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