The attempted robbery took place in the city at around 4.45pm on 27 February.
A Humberside Police spokesman today said: "A woman was walking along Tilworth Road in Hull when a young man on a bike came up behind her and tried to snatch her bag from her shoulder, he failed and the bag fell to the ground.
"The woman was unharmed but shaken by the incident and we are appealing for anyone who saw this happen or has information that would help with our enquiries."
The man was described as white, in his late teens or early 20s, and wearing a light grey hoody, tracksuit bottoms and a woollen striped beanie hat.
Police said the would-be robber was riding a bright pink child's bike with white wheels.
Anyone with information is asked to call Humberside Police on 101, quoting log 334 27/02/18.