Rosalynn Carter, Michelle Obama, Hillary Clinton, George Bush and Nancy Reagan at the funeral of the former first lady Betty Ford. Photograph: Handout/Getty Images

US first ladies past and present have joined other former White House residents to remember Betty Ford at her funeral.

Speakers hailed Ford for reshaping the role of first lady with her plain-spoken candour and as an inspiration for the addiction rehabilitation centres that bear her name.

"Millions of women are in her debt today and she was never afraid to speak the truth even about the most sensitive subjects, including her own struggle with alcohol and painkillers," said Rosalynn Carter, who succeeded her in the White House. "She got some criticism, but I thought she was wonderful and her honesty gave to others every single day."

Michelle Obama, Nancy Reagan, Hillary Clinton and former president George Bush were among those at the service in Palm Desert, California.

Ford, who died aged 93 on Friday, helped bring previously taboo subjects such as breast cancer into public discussion and openly discussed her own battle with the disease. She was equally candid about her struggles with drug and alcohol abuse, and spearheaded the Betty Ford Centre to treat those addictions.

Cokie Roberts, a TV interviewer, noted that Gerald Ford confided to her privately that his wife badgered him relentlessly into stronger public support of equal rights for women.

Bush, accompanied by Nancy Reagan, arrived a few minutes before Michelle Obama. The former president chatted quietly with Reagan as they waited for the services to begin, greeting Clinton as she took a seat next to him.

After the funeral, members of the public were invited to file past the casket and sign a guest book.

Ford's body will be flown on Wednesday to Grand Rapids, Michigan, where Lynne Cheney, wife of the former US vice-president Dick Cheney, and historian Richard Norton Smith will speak at a church service. The former first lady Barbara Bush is expected to attend that event.

Ford will be buried alongside her husband at Gerald Ford's presidential museum in Grand Rapids on Thursday, which would have been his 98th birthday.

Ford, the accidental first lady, was thrust into the White House when Richard Nixon resigned as US president over the Watergate scandal and Gerald Ford, then vice-president, assumed the US's highest office.

Rosalynn Carter recalled that she met Ford when the first lady visited Georgia, where Carter's husband was governor.

"We invited Betty to stay at the governor's mansion. She was the most distinguished guest we had ever had but when she arrived she was so warm and friendly that she immediately put me at ease and we had a good time together.

"Of course I didn't tell her then that my husband was thinking of running for president," Carter added.

A lifelong friendship remained intact after Gerald Ford lost his re-election bid to Jimmy Carter.

Outside the church passersby, some walking dogs or out for a jog, stopped to reflect on the former first lady's life.

"I don't know where a lot of people would be if it weren't for her," said Randy Gaynor, 47, a recovering alcoholic. "There's been a lot of first ladies and they did a lot of things, but this will be long remembered after she's gone."