Sweeney had used Bockscar for more than 10 training and practice missions (it wasn’t Bock’s airplane after all, just named after him). The answer relates to the purposes of the planes for each occasion.
The question relates to why didn’t Captain Frederick Bock fly his own plane (Bockscar) during the second run. Fewer people are aware that Bockscar (sometimes called Bock’s Car) delivered the second nuclear weapon, Fat Man, to Nagasaki on August 9, 1945. Most people are aware that the bomber Enola Gay delivered the first atomic weapon to Hiroshima.