How many nuclear bombs did the US have after the Japanese surrender?

Probably only the one that had been built just before the Nagasaki bombing but had not yet left the country when the Japanese surrendered.

While the Manhattan Project had plans and facilities to make a total of 24 atomic bombs by the end of 1945, after the war ended the priority to continue operating these facility dropped. Declassified documents show that actual production in 1945 was only 5 atomic bombs and of these 3 had already been detonated (i.e. Trinity, Hiroshima, Nagasaki) resulting in a stockpile at the end of 1945 of just 2 atomic bombs (i.e. one produced before the surrender, one produced after the surrender).

Even as late as 1947 when the Manhattan Project came to an end and the Atomic Energy Commision took over the stockpile was only 13 atomic bombs, and none of these were complete they were just kits of parts that would have to be assembled by hand in the field by an assembly team of trained specialists over a period of 3 days before the bomb could be used. The Atomic Energy Commision also discovered that no such assembly teams existed and there were no plans to train people in the specialized skills they would need to work on these assembly teams.

When President Harry S. Truman was informed of all this by the Atomic Energy Commision it is said that his face turned completely grey! Since the end of the war he had been concentrating on balancing the Federal Budget by gutting the conventional military and depending 100% on atomic bombs to defend the US... and now he essentially was informed that he had neither a conventional nor a nuclear defense!