So far as I can tell, the 39th Congress (the one that proposed the 14th Amendment) did not pass a law explicitly providing that schools in DC must be segregated. No Congress passed such a law. However, Congress did pass laws that referred to "white schools" and "colored schools," and the 39th Congress passed a couple of these laws.

In Bolling, it was actually disputed between the two sides whether or not acts of Congress actually required segregation. The President's Committee on Civil Rights in 1947 concluded that

The core of Washington's segregated society is its dual system of public education. It operates under congressional legislation which assumes the fact of segregation but nowhere makes it mandatory.

On the other hand, in Carr v. Corning, the Court of Appeals for the DC Circuit considered the question of whether or not DC school segregation was permissible, and whether it was required by Congress. They concluded it was allowed, and cited acts of Congress dating back to 1862 that discussed segregated schools. I'll try to summarize that discussion.

In 1862, the law setting up DC public schools contained a special tax "for the purpose of initiating a system of education of colored children." Later that year, Congress directed the board of trustees "to provide suitable rooms and teachers for such a number of schools as, in their opinion, will best accommodate the colored children;" later still, it set up a separate board for colored schools. In 1864, Congress said:

That any white resident of said county shall be privileged to place his or her child or ward at any one of the schools provided for the education of white children in said county he or she may think proper to select, with the consent of the trustees of both districts, and any colored resident shall have the same rights with respect to colored schools.

That provision was reenacted in 1874 when Congress was doing a general codification of DC law. It wasn't reenacted in a 1901 codification, which ordinarily might have meant it was repealed, but the DC Circuit concluded it was not. Post-1901 laws provided for two assistant superintendents, one for white schools and one for colored schools.

Even after Carr, the briefs in Bolling disputed whether or not segregation was required by Congress. However, the overall picture should be fairly clear: Congress clearly assumed that the schools would be segregated and passed laws consistent with that. The most natural reading of these laws is that schools should generally be segregated. However, Congress doesn't seem to have passed a law explicitly saying "white children may only go to white schools and colored children may only go to colored schools;" if it had, the Carr court or one of the Bolling briefs would probably have mentioned it.

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So that's a general overview, but you asked specifically about the 39th Congress. They passed a total of two laws on this topic (at least, that's all the Carr court could dig up and I didn't see anything else when Ctrl+Fing my way through the statutes):

That the eighteenth section of the act entitled "An act to provide for the public instruction of youth in the county of Washington, District of Columbia, and for other purposes," approved June twenty-five, eighteen hundred and sixty-four, shall be so construed as to require the cities of Washington and Georgetown to pay over to the trustees of colored schools of said cities such a proportionate part of all moneys received or expended for school or educational purposes in said cities, including the cost of sites, buildings, improvements, furniture, and books, and all other expenditures on account of schools, as the colored children between the ages of six and seventeen years, in the respective cities, bear to the whole number of children, white and colored, between the same ages.

and

That the commissioner of public buildings be, and he is hereby, authorized and required to grant and convey to the trustees of colored schools for the cities of Washington and Georgetown, in the District of Columbia, for the sole use of schools for colored children in said District of Columbia, all the right, title, and interest of the United States in and to lots numbered one, two, and eighteen in square nine hundred and eighty-five, in the said city of Washington, said lots having been designated and set apart by the Secretary of the Interior to be used for colored schools. And whenever the same shall be converted to other uses, they shall revert to the United States.

As you can see, there's nothing there that explicitly commands segregation. The laws setting up a separate school board for colored schools already existed. But they were at the very least acting within the preexisting system of segregated schools.