First, you've got your timeline a bit off. Using Japanese time zones, Hiroshima was August 6th, Nagasaki was August 9th, Hirohito broadcast the acceptance of the Potsdam terms on August 15th.

As for a lack of a third bomb: the US had two bombs ready to go at the end of July/early August. They had a third in the pipeline ready for around August 17th or 18th. However on August 10th, Truman issued an order that no further atomic bombings would happen unless he approved of them personally. His reasons for this were mixed: there were rumblings that the Japanese were considering surrender; he had just heard about the high casualties at Hiroshima and considered them appalling (there is reason to suspect he did not realize how many civilians would be killed); and it also became acute to him that the decisions of when to drop the bomb were being made by soldiers in the field (out of his control).

During the period between August 9th and August 15th, the US was in negotiations with the Japanese and trying to force them to accept unconditional surrender. They did conduct several massive conventional bombing raids to continue this. There was a question of whether another atomic bombing raid might be warranted. But it did not come to anything, because by the time the next would have been ready, even if Truman had approved it (which he never did), the Japanese had surrendered.