The woman was walking along Somerset Road in Almondbury when she was approached from behind by a man who grabbed hold of the bag.
During the struggle, the victim hit her head on the vehicle and fell to the floor.
The man left empty-handed, walking off down Somerset Road towards the bus stop by the mini roundabout at the end of Longley Lane. He reportedly walked in the middle of the road and a number of cars beeped their horns to get him to move.
Police today released a description of the man they want to trace following the attempted robbery on Tuesday between 6.30am and 6.35am.
The suspect is described as an Asian male, in his twenties, about 5ft 6in and slim, with short straight black hair and a stubbly beard. He wore dark trousers and a dark jacket, which was a bit longer than waist length.
Detective Constable Seb Morgan, of Kirklees District CID, said: “This was understandably a very concerning incident for the victim. She has been shouting and screaming throughout, which we believe has in part caused the suspect to walk away, and we are keen to speak to anyone who has seen or heard any part of this incident.
“We understand that following this attempted robbery, the man involved has been walking in the middle of the road, attracting the attention of a number of motorists who have beeped their horns to try and get him to move. We are keen to speak to any of these people who may be able to assist with information about this man and his movements after this offence.”
Anyone with information is asked to call Kirklees District CID via 101 or to pass information anonymously to independent charity Crimestoppers on 0800 555 111.