It is hard to generalize an entire population. But in general the initial responses were excitement and enthusiasm (because they associated it with the end of the war), tempered with a question of what was going to happen next. These editorial cartoons from the first few weeks of the bomb give a sense of the range of views expressed in major newspapers.

As for diplomatic efforts, the US did attempt to push for what was called "international control," which would involve basically having the UN guarantee that nobody (including the USA) would make nuclear weapons. The Baruch Plan of 1946 would basically allow the UN to inspect any country to make sure they weren't developing the plants you need to make nuclear arms, and once inspections were in place, the USA would get rid of its own nuclear weapons. This did not get very far, because the Soviets did not appreciate the asymmetry of it (they would have to be disarmed before the US would be disarmed) and because the Soviets were working on their own bomb by this time (trusting it more than the new UN to keep the peace).