The 16-year-old has been bailed until May 31, pending further inquiries.
The robbery happened between 3.30pm and 3.45pm on Thursday, March 12, when the victim, a bus driver, was driving the bus through Brookside when she stopped at a bus stop adjacent to Bembridge.
Police say a male got on to the bus and handed over money for the fare to the driver, who, as is policy, checked the note with an ultra violet torch which showed it was counterfeit.
A spokesman said: "The male reached through the gap in the plastic security glass of the driver's cabin and grabbed the bus driver's hand which was holding the money and took the money back from her as well as a handful of £1 coins. He then ran off from the scene."
The arrest comes after police issued an appeal for information with CCTV images from the bus. The spokesman said police would like to thank everyone who shared the original CCTV appeal.