It wasn't until 1958 that the U.S. military deployed the Redstone ballistic missile; before that time, all nuclear weapons had to be delivered by bomber.

By the end of August 1945 the USAAF had already developed a hypothetical nuclear attack plan that would result in the total destruction of the USSR, given adequate nuclear weapons (which they did not have). You can read the plan and view a map of its targets here, and here is a map from the same report about the use of foreign bases to attack Soviet targets. Logistically speaking, it was not until 1948 that B-29s were moved to the European theatre so that, if necessary, they could target Moscow on relatively short notice. Some details on US bomber and bomb movements are here.