Last August, Ms. Bishop was one of three candidates who vied for the party’s leadership after Malcolm Turnbull, who was then the prime minister, was ousted in a back-room revolt. Despite having higher public approval ratings than her two male opponents, she lost on the first ballot with less than 13 percent of the vote. Scott Morrison, who was then the treasurer of Australia, was elected by Liberal Party lawmakers as the next prime minister.

After the vote, Ms. Bishop opted to leave the cabinet and become a rank-and-file lawmaker.

Ms. Ford said she did not think “it even occurred” to male party members to elect a woman as their leader. Ms. Bishop was the first woman to formally stand for leader of the Liberal Party.

“She was hugely popular with the electorate,” Ms. Ford said. “To ignore not only her skills and ability and merit, but to do it so blatantly, must have been a huge slap in the face for her.”

Ms. Bishop’s loss in the leadership vote sent waves of relief through the opposition Labor Party, which is favored in polls to win the next election. Though the exact date has not been set, elections must be held this year.

If Ms. Bishop had won, the Labor Party “might have had a real fight on their hands in the next election,” said Jane Caro, an Australian author and commentator. “So the Liberal Party really cut off its own nose to spite its face, but such is the strong belief among many conservative people that women should not be in charge.”