Crowdshipping has recently emerged as a sustainable option for urban parcel delivery, where transport tasks are carried out by regular citizens who are engaged in a passenger trip, instead of the usual professional carriers. A key challenge for such as service offering is to maintain a sustainable network of customers (demand) and couriers (supply). This paper quantitatively explores how demand and supply functions for bicycle crowdshipping meet in a parcel delivery market. Earlier literature has identified factors that determine the success of this business model. We build on this to estimate the potential of the new services, by means of a market equilibrium model. A case study is presented from the Netherlands which uses tailor-made surveys, bicycle trip data and online shopping statistics. The study quantifies the importance of influencing factors. The insights can be used to design a bike crowdshipping platform which brings together the demand and the supply sides effectively. Future research could go into platform design, more accurate behavioral models as well as into advanced pricing approaches.