Admiral Grace Hopper (an early computing pioneer better known for inventing COBOL) liked to tell a story in which a technician solved a glitch in the Harvard Mark II machine by pulling an actual insect out from between the contacts of one of its relays, and she subsequently promulgated bug in its hackish sense as a joke about the incident (though, as she was careful to admit, she was not there when it happened). For many years the logbook associated with the incident and the actual bug in question (a moth) sat in a display case at the Naval Surface Warfare Center (NSWC). The entire story, with a picture of the logbook and the moth taped into it, is recorded in the "Annals of the History of Computing", Vol. 3, No. 3 (July 1981), pp. 285-286.
The text of the log entry (from September 9, 1947), reads "1545 Relay #70 Panel F (moth) in relay. First actual case of bug being found". This wording establishes that the term was already in use at the time in its current specific sense -- and Hopper herself reports that the term `bug' was regularly applied to problems in radar electronics during WWII.