To work towards an advanced model of the bicycle-rider-environment system, an open-loop bicycle-rider model was developed in the commercial multibody dynamics software ADAMS. The main contribution of this article to bicycle dynamics is the analysis of tyre and rider properties that influence bicycle stability. A system identification method is used to extract linear stability properties from time domain analysis. The weave and capsize eigenmodes of the bicycle-rider system are analysed. The effect of tyre properties is studied using the tyre’s forces and torques that have been measured in several operating conditions. The main result is that extending simplified models with a realistic tyre model leads to a notable decrease in the weave stability and a stabilization of the capsize mode. This effect is mainly caused by the twisting torque. Different tyres and tyre inflation pressures have little effect on the bicycle’s stability, in the case of riding straight at a constant forward speed. On the other hand, the tyre load does have a large effect on bicycle stability. The sensitivity study of rider properties shows that body stiffness and damping have a small effect on the weave and capsize mode, whereas arm stiffness destabilizes the capsize mode and arm damping destabilizes the weave mode.