The suspect is described as 5ft 11in tall with short dark hair. He was wearing a dark tracksuit style top, black tracksuit bottoms and black trainers. He was riding a dark bicycle.
The force has released an image of a man they would like to speak to in connection with the incidents.
The police would particularly like to identify a woman who was seen on CCTV being approached by the man on his bike at 8.23am on Hill Street.
Anyone with information is being asked to phone the States police on 612612 or Crimestoppers on 0800 555 111.