The family of a New Zealand woman fighting for her life in a Bali hospital are "gobsmacked" that generous Kiwis have already donated $48,000 towards her medical bills.

Hamilton woman Abby Hartley remains in an induced coma in hospital in Nusa Dua, Denpasar with her husband Richard and two children by her bedside.

She fell ill the day the couple arrived in Bali for a holiday.

Hartley suffered a twisted bowel, which had impacted on blood flow. She required emergency surgery and, despite the success of the operation, she went on to develop acute respiratory distress syndrome.

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The family created a Givealittle page 24 hours ago to help cover the $70,000 in bills racked up after their insurance company refused to pay.

Richard said she would be under sedation for the next four weeks while a rare antibiotic attempted to fight back.

He said her condition had been very up and down since she landed in hospital.

"She starts to improve and then you get false hope and it goes down hill again but we are hanging in there."

He said he been absolutely "gobsmacked" by the amount of support the family had received despite their insurance company not being able to cover the costs of rising medical bills.

In the last 24 hours more than $43,000 has been raised on a Givealittle page set up by Hartley's daughter Sophie.

"We never expected it. Initially we thought we might get near $10,000 to cover a few bits and pieces but to get that amount in such short period of time is gobsmacking.

"We've had an absolutely amazing reaction from people in Bali offerings us accommodation, to friends in the UK and all those Kiwis back home."

Hartley has also struggled with a collapsed lung following a severe chest infection and has been in hospital since August 1.

"Our mum is fighting for her life in ICU in a hospital in Bali and unfortunately insurance company is refusing to cover any medical costs," daughter Sophie said.

"After a very long and stressful battle with the insurance company they have made the final decision to not cover any medical costs therefore we have been left with a very expensive medical bill.

"Her medical bill includes 24/7 care and observation, all medications etc," she added.

Richard said that due to a pre-existing medical condition Hartley once had, the insurance company refused to pay.