After Holt's disappearance in December 1966, Bury was one of four candidates to contest the Liberal leadership ballot, along with John Gorton, Paul Hasluck, and Billy Snedden. He had some support within the party, including from Peter Howson, and was reportedly Menzies' second most preferred candidate after Hasluck. According to Graham Freudenberg much of his support was due to his status as the only candidate from New South Wales. However, he was virtually unknown among the general public and was not seen as a strong television performer. Bury polled an estimated 16 votes (out of 81) on the first ballot, ahead of only Snedden. Both were eliminated and Gorton went on to defeat Hasluck in the final ballot.