Bevan's mother Rachel Fortune, 59, said: "My beautiful daughter and granddaughter are now at peace.
"The family would like to thank all the friends of Pascal, Charlotte and Zaani, some of whom we have only met today."
University Hospitals Bristol NHS Trust is coming under growing pressure to explain why Bevan was not challenged as she left the hospital wearing just slippers and cradling the 4-day-old child in a blanket.
It is believed that Bevan, 30, had suffered from schizophrenia and depression. Investigators will look at whether she may have made changes to medication she was taking so that she could breastfeed her baby.
A report by health watchdog the Care Quality Commission published this week said the hospital was "an impressive and highly functional unit".
But it said when its inspectors visited, teams and individuals were having to "manage and mitigate the risks of working with a lower than optimal midwife-to-birth ratio".
The trust said patients were free to come and go from its hospitals unless there were legal restrictions on their movements.
Patients can release the doors from the inside to let themselves out. There is CCTV in wards and public areas. It is not monitored but can be reviewed later.
The spokeswoman added that the trust had guidelines to aid professionals in "the screening, detection and management of women with mental health problems in antenatal and postnatal settings".
A member of the public had first raised the alarm after spotting hospital slippers and a baby blanket at the top of the cliff.
On Wednesday, Bevan's boyfriend Pascal Malbrouck revealed she had suffered from schizophrenia and depression in the days following the birth, and was sleep-deprived.
It is also believed she might have stopped taking her medication so that she could breastfeed her newborn. Yet CCTV footage from the hospital showed her walking through security gates and past at least four nurses without anyone stopping her. She was not wearing a coat or any shoes, and she was clutching her baby wrapped only in a blanket.
The hospital has now launched a "thorough review" into how Bevan was allowed to leave the ward unchallenged.
Her friend Jessie Saul, 20, told the Telegraph hospital staff knew Bevan had problems with her mental health, and should have kept a closer eye on her.
She said: "There's meant to be people on that desk 24 hours a day. Someone should have stopped her - they knew she was a risk.
"They just let her walk straight out. It's ridiculous - they completely failed her. I hope they make serious changes so this is never allowed to happen again."
Although it appears Bevan was looking forward to the birth of her baby, her Facebook profile reveals she fought a long battle against mental illness. She had regular contact with NHS mental services, which would have shown up in her records when she entered hospital to give birth.
In 2011, she told a friend how she was having difficulties with a partner because she was "hearing voices and nasty stuff". Earlier, she complained she was being "detained against her will" at a psychiatric hospital in Taunton, Devon.
Hours before she vanished, her Facebook profile suggests Bevan watched a video entitled Get Through Positive and Negative Thinking Rough Patches. Yet she had also recently posted happy pictures of herself posing in patterned dresses with her baby bump.
Local mothers took to the police Facebook page to express surprise and concern that Bevan was allowed to walk out of the hospital.
New mother Jo Burston said: "I gave birth to my baby five days ago at Bristol's Southmead hospital. I walked my baby down to reception so I could see my mum and dad and on the way down I was grilled by four members of staff.
"And I'm not in a vulnerable position like Charlotte was. So yes, I do think the hospital let her down."
