Creating highly realistic Virtual Reality (VR) bicycle experiences can be time-consuming and expensive. Moreover, it is unclear what hardware parts are necessary to design a bicycle simulator and whether a bicycle is needed at all. In this paper, we investigated cycling fidelity and control of VR bicycle simulators. For this, we developed and evaluated three cycling simulators: (1) cycling without a bicycle (bikeless), (2) cycling on a fixed (stationary) and (3) moving bicycle (tandem) with four levels of control (no control, steering, pedaling, and steering + pedaling). To evaluate all combinations of fidelity and control, we conducted a controlled experiment (N = 24) in indoor and outdoor settings. We found that the bikeless setup provides the highest feeling of safety, while the tandem leads to the highest realism without increasing motion sickness. Moreover, we discovered that bicycles are not essential for cycling in VR.