My paper about the calculation of the unitary part of the Bures measure was recently accepted for publication
Renan Cabrera, Herschel Rabitz, Calculation of the Unitary part of the Bures Measure for N-level Quantum Systems , Accepted at J. Phy A: Math. Theor.
This paper shows how the Bures measure can be expressed as the product of the measure of even euclidean balls. This means that we now have a simple and easy formula for sampling. The ultimate application will be in Bayesian quantum estimation.
My wikipedia article that explains the basics of the Bures metric is