Minimising opposing forces is a matter of interest to most cyclists. These forces arise from passage through air (``drag'') and interaction with the road surface (``resistance''). Recent work recognises that resistance forces arise not only from the deformation of the tyre (``rolling resistance'') but also from irregularities in the road surface (``roughness resistance''), which lead to power dissipation in the body of the rider through vibration. The latter effect may also have an adverse impact on human health. In this work we offer a quantitative theory of roughness resistance and vibration that links these effects to a surface characterisation in terms of the International Roughness Index (IRI). We show that the roughness resistance and the Vibration Dose Value (or VDV, the usual vibration dosage metric) can be expressed in terms of elementary formulae. The roughness resistance depends only on the vertical stiffness of the bicycle and the roughness index. Surprisingly, other apparently relevant parameters, such as physiological characteristics of the bicycle rider and other features of the bicycle, do not enter. For roads of moderate roughness, roughness resistance is larger than rolling resistance. For very rough roads, roughness resistance is larger than aerodynamic drag. So only on roads of high quality (in most jurisdictions, accounting for less than 10~\% of the total) can roughness resistance be ignored. Roughness resistance can be mitigated by reducing the vertical stiffness of the bicycle. In common with other recent reports, we find that almost any cycling activity will breach public health guidelines relating to Vibration Dose Value.