The offender was on a small blue Honda motorcycle with colourful graphics, believed stolen, Gosnells police officer-in-charge Senior Sergeant Ray Thompson said.
The man tried to grab the bag off her shoulder but she held on to it, though she fell in the process.
The man was thin, with dark eyes and skin, black pants and jacket, and no helmet.
Police believe he has committed other offences in the area.
Sgt Thompson urged shoppers using the centre to be careful.