But federal prosecutors allege the Sydney executive hid a secret - her extravagant presents totalling millions of dollars were paid for by NAB.

The chief executive of events and human resources company Human Group, 47, pleaded not guilty on Monday to dozens of fraud and bribery charges alleging she masterminded a multi-million-dollar scam against the Big Four bank between 2013 and 2017.

Invoices were made out to look like NAB expenditures, the Crown alleges, including for a Toyota Kluger for Rosamond's in-laws and a $30,000 fuel bill for a family member's trucking company.

Rosamond allegedly offered money or other items "as gifts from herself, when in fact she had every intention for NAB to foot the bill," crown prosecutor Katrina Mackenzie told a Sydney District Court jury on Monday.

One witness is expected to say that when they inquired, Rosamond told them: "Don't worry, I'm not paying for it."

Rosemary Rogers, the chief-of-staff to the bank's then-chief executive, allegedly played a key role in the scam, by ensuring the fraudulent invoices continued to be paid by bank staff.

For her part, she received benefits including a $620,000 trip with extended family to New York, Miami and other US cities in 2014 that included transfers by private jet and yacht, the jury heard.

"The holiday was worth a considerable amount of money and was allocated to 'NAB Project 27'," Ms Mackenzie said.

"Why? We say it was to conceal where the money was really going."

Rogers, who is expected to give evidence in the crown case later in the trial, allegedly also received a $130,000 boat and mooring in Melbourne and regular trips to a secluded resort in NSW's Wolgan Valley.

Rosamond allegedly took her own family on a $132,000 holiday to the Rocky Mountains in the US, which was coded as a NAB business trip and drawn down against the bank's prepaid account with Human Group.

Among the largest of the allegedly fraudulent invoices issued was one for $2.2 million.

It was purportedly for "Project Eagle" - the codename for the onboarding of former NSW premier Mike Baird as an NAB executive in 2017 - but instead was to cover a substantial amount for a home Rogers had purchased in Williamstown in Melbourne's west.

An extra $700,000 allegedly went to Rosamond, Ms Mackenzie expects the evidence to show.

Rosamond's lawyer, Dr Anton Hughes, is due to give his opening later in the week.

The trial continues.

Australian Associated Press