I found this. Maybe it would have direct records of the Act?
It is from the Congressional Globe, which recorded all business of Congress up through about 1874 (now the journal is called the Congressional Record). It has lots of search devices, but I’m not sure what exactly I’m looking for. I couldn’t find an actual “Bank Act of 1871” but it might have a different name so maybe I’m looking for the wrong item.
https://memory.loc.gov/ammem/amlaw/lwcglink.html
“The District of Columbia Organic Act of 1871 is an Act of Congress that repealed the individual charters of the cities of Washington and Georgetown and established a new territorial government for the whole District of Columbia.”