We present new central stellar velocity dispersions for 484 Sy 1.9 and Sy 2 from the second data release of the Swift/BAT AGN Spectroscopic Survey (BASS DR2). This constitutes the largest study of velocity dispersion measurements in X-ray selected, obscured AGN with 956 independent measurements of the Ca H+K and Mg b region (3880-5550A) and the Ca triplet region (8350-8730A) from 642 spectra mainly from VLT/Xshooter or Palomar/DoubleSpec. Our sample spans velocity dispersions of 40-360 km/s, corresponding to 4-5 orders of magnitude in black holes mass (MBH=10^5.5-9.6 Msun), bolometric luminosity (LBol~10^{42-46 ergs/s), and Eddington ratio (L/Ledd~10^{-5}-2). For 281 AGN, our data provide the first published central velocity dispersions, including 6 AGN with low mass black holes (MBH=10^5.5-6.5 Msun), discovered thanks to our high spectral resolution observations (sigma~25 km/s). The survey represents a significant advance with a nearly complete census of hard-X-ray selected obscured AGN with measurements for 99% of nearby AGN (z<0.1) outside the Galactic plane. The BASS AGN have higher velocity dispersions than the more numerous optically selected narrow line AGN (i.e., ~150 vs. ~100 km/s), but are not biased towards the highest velocity dispersions of massive ellipticals (i.e., >250 km/s). Despite sufficient spectral resolution to resolve the velocity dispersions associated with the bulges of small black holes (~10^4-5 Msun), we do not find a significant population of super-Eddington AGN. Using estimates of the black hole sphere of influence, direct stellar and gas black hole mass measurements could be obtained with existing facilities for more than ~100 BASS AGN.