They followed the customer up Queen Street and into Victoria Street before returning to the terminal after being told police would not attend.
The authority said the customer, who had recently recovered from cancer, later laid a complaint with Fullers against Ms Bailey and her colleague for following her and making loud derogatory comments.
Attached to her complaint was her ferry ticket, which she found lodged in a shoe in her bag.
The customer also laid a complaint of intimidation with police.
In her complaint to Fullers, the customer said she was chased and was called a "thief", "white trash" and "loopy".
During an investigation into the complaint, Ms Bailey explained that she followed the customer because she had been advised to do so by her supervisor.
The authority said Ms Bailey denied calling the customer a "thief", but acknowledged she called her "crazy".
She said she believed she was put in a position where she had to deal with a situation she was not trained to deal with and where no company policy was in place.
The authority said Fullers found that Ms Bailey had breached standards of behaviour, and she was issued with a final written warning.
Ms Bailey said that warning unjustifiably disadvantaged her employment but authority member Vicki Campbell said she was satisfied the investigation into Ms Bailey was fair.
"Fullers reached a reasonable conclusion that Ms Bailey's actions in following the customer off the worksite without authorisation, and reminding the customer that what she had done was theft constituted serious misconduct in that it was intimidating and harassment.
"Ms Bailey's actions were also demonstrative of poor customer service."
Ms Campbell said the decision to give her a final written warning was fair and reasonable and that she was not subjected to an unjustified disadvantage in her employment.
Costs were reserved.
Comment was being sought from Fullers and Ms Bailey.
