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.
PerthNow Digital Edition.
Your local paper, whenever you want it.Get in front of tomorrow's news for FREE
Journalism for the curious Australian across politics, business, culture and opinion.
READ NOWPolice believe he has committed other offences in the area.
Sgt Thompson urged shoppers using the centre to be careful.