When Penguin's henchmen see the Batcycle coming towards them, they refer to Batman & Robin as "ghosts", something that Robin makes reference to later. But given the great distance the Batcycle was from the henchmen, there is no way Robin could've heard the comment.
Batman and Robin claim to be spying on the Penguin using a TV camera hidden behind the fuel gauge in the Batmobile. However, the angle of the shot indicates that the camera is outside the passenger door.
After Batman and Robin catch up with Penguin and his henchmen - who have possession of the Batmobile - they are on the Batcycle. After a successful capture, they are seen driving the Batmobile with the criminals tied to the hood. It's obvious they left the Batcycle behind.