Angel Delgado, 29, of 54 Cooper St., Shoreham, was charged with first-degree robbery.
Responding officers saw a man who matched the description of the bank robber riding a bicycle south on Station Road in Medford.
After the officers told Delgado to stop, he jumped off the bicycle and ran into nearby woods, police said. He was captured after a short foot pursuit, police said.
Delgado was to be arraigned in First District County Central Islip on Wednesday.