Bernice Louise Marychurch was killed on the Number 74 bus on Wednesday around 2.30pm.
The man charged with her murder, 37-year-old Kael Leona, appeared in the Auckland District Court on Friday morning after handing himself into police on Thursday.
Auckland City relieving district crime manager, Acting Detective Inspector Alisse Robertson, said police were still working to establish the victim's movements on the day she died and were seeking the public's help.
"Police continue to establish the victim's movements and now believe she may have known the man charged with her murder."
Robertson said they were reviewing a range of CCTV footage in the Panmure and Onehunga area between 8.30am and 1.30pm on 23 October, which showed the victim with a man at several points throughout the day.
He said they wanted to hear from anyone who was in the following areas and times:
• Outside Woolworths Onehunga, about 8.30am
• Boarding a bus on Church Street, Onehunga at about 9am and disembarking at 9.30am at a bus stop on Tripoli Road, Panmure
• Between 1.30pm and 2pm, in the Panmure township and it's bus station
• About 2pm, boarding the No.74 Bus at the Panmure Bus Station.
• baseball cap with Niue written across the front
• A zip-up camo coloured hooded sweatshirt
• A light coloured pants and white shoes
• Carrying a black backpack.
"The victim was wearing a grey hooded sweatshirt, light coloured shorts, black shoes and carrying a black satchel," Robertson said.
Earlier this week, Police Minister Mark Mitchell said there would be a greater police presence across public transport in Auckland.
He said it was a senseless and horrific attack and people deserve to safe on buses, trains and ferries.
Anyone with any information could contact police by calling 105 using reference number 241023/8926, or by making an online report at 105.police.govt.nz.
