The incident happened in the car park of Morrisons on East Somerset Way at about 11am.
The victim had placed her bag in a shopping trolley next to her car when a man ran past and stole it.
He then ran towards the fuel station and got into a black Toyota Corolla before driving off at speed.
PC Tom Giles said: “It is awful to think someone can deliberately target a vulnerable elderly woman in this way. The victim has been left incredibly scared and shaken by this incident and officers have followed up with her at home to make sure she is ok and has all the support she needs. We’re reviewing CCTV and making enquiries to identify the registered keeper of the Toyota seen driving away from the scene.
“We’re also keen to hear from anyone who was in the car park at the time who can help us identify the offender as well as anyone who saw anything suspicious.”
If you can help, call 101 and give the call handler the reference 5222179033.