  We obtain two sided estimates for the Bures volume of an arbitrary subset of
the set of $N\times N$ density matrices, in terms of the Hilbert-Schmidt volume
of that subset. For general subsets, our results are essentially optimal (for
large $N$). As applications, we derive in particular nontrivial lower and upper
bounds for the Bures volume of sets of separable states and for sets of states
with positive partial transpose.
  PACS numbers: 02.40.Ft, 03.65.Db, 03.65.Ud, 03.67.Mn
