  Black Hole Low Mass X-ray Binaries (BH-LMXBs) are excellent observational
laboratories for studying many open questions in accretion physics. However,
determining the physical properties of BH-LMXBs necessitates knowing their
distances. With the increased discovery rate of BH-LMXBs, many canonical
methods cannot produce accurate distance estimates at the desired pace. In this
study, we develop a versatile statistical framework to obtain robust distance
estimates soon after discovery. Our framework builds on previous methods where
the soft spectral state and the soft-to-hard spectral state transitions,
typically present in an outbursting BH-LMXB, are used to place constraints on
mass and distance. We further develop the traditional framework by
incorporating general relativistic corrections, accounting for
spectral/physical parameter uncertainties, and employing assumptions grounded
in current theoretical and observational knowledge. We tested our framework by
analyzing a sample of 50 BH-LMXB sources using X-ray spectral data from the
\swift/XRT, \maxi/GSC, and \rxte/PCA missions. By modeling their spectra, we
applied our framework to 26 sources from the 50. Comparison of our estimated
distances to previous distance estimates indicates that our findings are
dependable and in agreement with the accurate estimates obtained through
parallax and H\,{\sc i} absorption methods. Investigating the accuracy of our
constraints, we have found that estimates obtained using both the soft and
transition spectral information have a median uncertainty (1$\sigma$) of 20\%,
while estimates obtained using only the soft spectral state spectrum have a
median uncertainty (1$\sigma$) of around 50\%. Furthermore, we have found no
instrument-specific biases.
