Bile acids comprise about 80% of the organic compounds in bile. We use this staining to detect bile in tumor cells, e.g. metastatic hepatocellular carcinoma.
The principle of Hall's stain is the producing a green, emerald pigment by combination of ferric chlorid to bilirubin or biliverdin. So I don't think, that can be used for specific demonstration of bile acids. But it can show you, where bile is located in the section.
Special stains for bile acids will not give you the answer. We use HPLC for detection of specific bile acids. A stain will be informative showing you the "load" of total bile acids and their production and of course distribution. Separation of certain bile acid "species" is a matter of other methods.