Yao Etienne, an Abidjan resident, acknowledges that Bedie's party is the one "that made this country."
"But it seems that they remain in the past," he said. "We all want the glory of the golden years back. But Bedie is too old. He had his chance and failed. Now this country needs to go forward."
His supporters, though, described Bedie's experience as an asset.
"Some people say that he is too old, but it is in the old pot that you cook the best stew," said 62-year-old Paul N'Guessan Kouassi.
Germaine Akra, 67, said youth wing leader and challenger Bertin Konan Kouadio was not ready to head the party.
"Nobody can fill the shoes yet. There is a new generation, but it is not their time yet," he said.
Bedie placed third in the country's disputed 2010 presidential election, taking about 25 percent of the vote. He then threw his support behind now-President Alassane Ouattara in the subsequent runoff vote.
Incumbent Laurent Gbagbo refused to accept Ouattara's victory, resulting in a standoff that claimed more than 3,000 lives before Gbagbo was arrested in April 2011.
Eighteen members of Bedie's party had tried to cancel the weekend convention through the courts, denouncing organizational irregularities and a perceived bias of the political office in favor of Bedie. On Wednesday, an Abidjan court stated that it did not have the jurisdiction to rule on that demand.