The woman suffered cuts and bruises after she refused to let go of the bag and was dragged on the ground by the cyclist.
Police said the attempted robbery occurred about 1.45pm on Thursday, 4 April, when the victim was walking along Newport Avenue.
When she refused to release her handbag, she was dragged to the ground and along the roadway, police said.
“As a car approached the suspect ran off empty handed, leaving the bag and his bicycle behind. The occupants of the car assisted the woman and the suspect was last seen running in the direction of Cay Court apartments,” according to a statement released by police Friday.
The woman, who suffered cuts and bruising to her legs and body, was taken to hospital and released following treatment.
The suspect is described as being of dark complexion with short hair, wearing jeans pants and had a blue towel around his head. He was riding a red and white bicycle.
Anyone who was in the area at the time and has any information which could assist the enquiry is asked to call George Town CID on 949-4222, the RCIPS tip-line 949-7777 or Crime Stoppers 800-8477 (TIPS).