If it is your habit to use handbag, hold it close to your body, not dangling from a hand or wrist.  Personally, I don’t think much of looping it over 1 shoulder either.  Any of these 3 ways to carry a handbag makes it easy to snatch.  I suggest wearing your bag diagonally, like a messenger bag, and carry it to one side or the front.  [If you carry it behind you, someone on the bus or subway could open it and you would never notice.]