As for the question how many bombs the USA had at that time, there is a transcript of a phone call available where some responsible general or some such at length explains that they are capable to produce 7 bombs over two months.
Except he keeps explaining it rather complicated on a per month basis, one month they can produce three ot four bombs. After a month producing four, the next month they are only able to produce three, and vice versa...
(I remembered 9 every two months, but adapted it to the numbers proviuded in the link below)
Edit: Googled a llitte bit, didn't find the transcript I had in mind, but a memorandum by general Groves:
Bomb Production Schedule 19454. The final components of the first gun type bomb have arrived at Tinian, those of the first implosion type should leave San Francisco by airplane early on 30 July. I see no reason to change our previous readiness predictions on the first three bombs. In September, we should have three or four bombs. One of these will be made from 235 material and will have a smaller effectiveness, about two-thirds that of the test type, but by November, we should be able to bring this up to full power. There should be either four or three bombs in October, one of the lesser size. In November, there should be at least five bombs and the rate will rise to seven in December and increase decidedly in early 1946.
Eidt 2: If you really want to dig into primary sources on the whole Manhattan Project, the politics around it, and even some MAGIC transcript of Japanese reactions, check this page out:
The Atomic Bomb and the End of WW2Edit 3: Here is the transcript of the telephone call I had in mind )from the list of documents in the link above):
Call Gen. Hull w. Col. Seaman August 13th 1945"One every ten days."