We employ a quasirandom methodology, recently developed by Martin Roberts, to estimate the separability probabilities, with respect to the Bures (minimal monotone/statistical distinguishability) measure, of generic two-qubit and two-rebit states. This procedure, based on generalized properties of the golden ratio, yielded, in the course of almost seventeen billion iterations (recorded at intervals of five million), two-qubit estimates repeatedly close to nine decimal places to $$\frac{25}{341} =\frac{5^2}{11 \cdot 31} \approx 0.073313783$$ 25341=5211·31≈0.073313783 . However, despite the use of over twenty-three billion iterations, we do not presently perceive an exact value (rational or otherwise) for an estimate of 0.15709623 for the Bures two-rebit separability probability. The Bures qubit–qutrit case—for which Khvedelidze and Rogojin gave an estimate of 0.0014—is analyzed too. The value of $$\frac{1}{715}=\frac{1}{5 \cdot 11 \cdot 13} \approx 0.00139860$$ 1715=15·11·13≈0.00139860 is a well-fitting value to an estimate of 0.00139884. Interesting values $$\big (\frac{16}{12375} =\frac{4^2}{3^2 \cdot 5^3 \cdot 11}$$ (1612375=4232·53·11 and $$\frac{625}{109531136}=\frac{5^4}{2^{12} \cdot 11^2 \cdot 13 \cdot 17}\big )$$ 625109531136=54212·112·13·17) are conjectured for the Hilbert–Schmidt (HS) and Bures qubit–qudit ($$2 \times 4$$ 2×4 ) positive-partial-transpose (PPT)-probabilities. We re-examine, strongly supporting, conjectures that the HS qubit–qutrit and rebit–retrit separability probabilities are $$\frac{27}{1000}=\frac{3^3}{2^3 \cdot 5^3}$$ 271000=3323·53 and $$\frac{860}{6561}= \frac{2^2 \cdot 5 \cdot 43}{3^8}$$ 8606561=22·5·4338 , respectively. Prior studies have demonstrated that the HS two-rebit separability probability is $$\frac{29}{64}$$ 2964 and strongly pointed to the HS two-qubit counterpart being $$\frac{8}{33}$$ 833 and a certain operator monotone one (other than the Bures) being $$1 -\frac{256}{27 \pi ^2}$$ 1-25627π2 .