We measure the clustering of a sample of photometrically selected luminous red galaxies around a low redshift (0.2<z<0.6) sample of quasars selected from the Sloan Digital Sky Survey Data Release 5. We make use of a new statistical estimator to obtain precise measurements of the LRG auto-correlations and constrain halo occupation distributions for them. These are used to generate mock catalogs which aid in interpreting our quasar-LRG cross correlation measurements. The cross correlation is well described by a power law with slope 1.8pm0.1 and r_0=6pm0.5 h^{-1} Mpc, consistent with observed galaxy correlation functions. We find no evidence for `excess clustering on 0.1 Mpc scales and demonstrate that this is consistent with the results of Serber et al (2006) and Strand et al (2007), when one accounts for several subtleties in the interpretation of their measurements. Combining the quasar-LRG cross correlation with the LRG auto-correlations, we determine a large-scale quasar bias b_QSO = 1.09pm0.15 at a median redshift of 0.43, with no observed redshift or luminosity evolution. This corresponds to a mean halo mass <M>~ 10^{12} h^{-1} M_sun, Eddington ratios from 0.01 to 1 and lifetimes less than 10^{7} yr. Using simple models of halo occupation, these correspond to a number density of quasar hosts greater than 10^{-3} h^{3} Mpc^{-3} and stellar masses less than 10^{11} h^{-1} M_sun. The small-scale clustering signal can be interpreted with the aid of our mock LRG catalogs, and depends on the manner in which quasars inhabit halos. We find that our small scale measurements are inconsistent with quasar positions being randomly subsampled from halo centers above a mass threshold, requiring a satellite fraction > 25 per cent.
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