Joanna Bewley's son Tom returned home from hospital for the first time on Saturday, at three weeks old.
And his 20-month-old brother Tom also spent seven weeks in the neonatal intensive care unit (NICU) after he was born at 29 weeks.
Mrs Bewley and her husband Nigel, of St George, were impressed by the care they received in the unit and are supporting the hospital's Precious Drops Campaign to set up a breast milk bank, to benefit babies whose mothers cannot feed them while they are in the unit. Women who give birth to very premature babies cannot always produce enough milk for their infants, which may miss out on the nutrients found in breast milk.
There used to be a human milk bank at Southmead but it closed in the Eighties. When milk is needed urgently at the NICU it has to be sent from Oxford or Birmingham.
The hospital needs to raise £65,000 to get the milk bank up and running and will then have to raise a further £100,000 in the next two years to keep it running and equipped.
Mrs Bewley's waters broke early with both of her sons. With Jack she went into labour but with Tom she had to have a Caesarean at 34 weeks and six days pregnant.
She said returning to NICU was "a bit like going home" after spending so long there with Jack.
She said: "There were lots of familiar faces when we went back.
"Everyone is nice and friendly there, although I don't think they expected to see us again.
"We have been very lucky with both of our sons, they have been very straightforward and we have been blessed with healthy babies."
Mrs Bewley, a publishing administrator, was able to express milk for both her sons in the NICU but spoke to other mums who had been unable to, or had found it difficult. The new Bristol Milk Bank would be based at Southmead Hospital, providing milk to its own NICU and to St Michael's Hospital.
People can support the campaign at an evening of skating at The Mall, Cribbs Causeway, on Thursday, December 10. To apply for tickets, call 01179 595562.