To answer my own question: Hans Kristensen, an expert on US nuclear forces said that the air force keeps a computerized command and control system that traces any movement of a nuclear weapon so that they have a complete picture of where they are at any given time.
He also added that perhaps what is most worrisome about this particular incident is that apparently an individual who had command authority about moving these weapons around decided to do so. Nuclear weapons are normally transferred on cargo planes, never on the wings of bombers, Kristensen said. Bomber flights with live nuclear weapons were ended in the late 1960s after accidents in Spain in 1966 and in Greenland in 1968.

