Type II Cepheids (T2Cs) are radially pulsating variables that trace old stellar populations and provide distance estimates through their period-luminosity (PL) relation. We trace the structure of old stars in the Bulge using new distance estimates and kinematic properties of T2Cs. We present new NIR photometry of T2Cs in the bulge from the VVV survey. We provide the largest sample (894 stars) of T2Cs with JHKs observations that have accurate periods from the OGLE catalog. Our analysis makes use of the Ks-band time-series to estimate mean magnitudes and distances by means of the PL relation. To constrain the kinematic properties of our targets, we complement our analysis with proper motions (PMs) based on both VVV and Gaia DR2. We derive an empirical Ks-band PL relation that depends on Galactic longitude and latitude: Ks0=(10.66+-0.02)-(2.21+-0.03)*(logP-1.2)-(0.020+-0.003)*l+(0.050+-0.008)*|b| mag; individual extinction corrections are based on a 3D reddening map. Our targets display a centrally concentrated distribution, with solid evidence of ellipsoidal symmetry--similar to the RR Lyrae (RRL) ellipsoid--and a few halo outliers up to >100 kpc. We obtain a distance from the Galactic center of R0=8.46+-0.03(stat.)+-0.11(syst.) kpc. We also find evidence that the bulge T2Cs belong to a kinematically hot population, as the tangential velocity components (sigma vl*=104.2+-3.0 km/s and sigma vb=96.8+-5.5 km/s) agree within 1.2sigma. Moreover, the difference between absolute and relative PM is in good agreement with the PM of Sgr A* from VLBA measures. We conclude that bulge T2Cs display an ellipsoidal distribution and have kinematics similar to RRLs, which are other tracers of the old, low-mass stellar population. T2Cs also provide an estimate of R0 that agrees excellently well with the literature, taking account of the reddening law.
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