Demand responsive transport (DRT) has received significant attention in recent years as a transport mode that can bridge the gap between personal motorized travel and public transport. It combines the best of individual cars and public transport: it can be more flexible, than traditional public transport, resembling the convenience of owning a car, but it does not come with the high cost of owning and maintaining a vehicle for the user. We conducted a stated preference (SP) survey about potential users’ preferences towards demand responsive transport at a rural Eastern European town in Hungary, Kiskunhalas, Hungary, and modelled individuals’ preferences towards DRT using a multinomial logit model. We had 6012 responses from a sample of 501 individuals, that was representative of the settlement with respect to age and gender. The results show that all else being equal, individuals find the DRT service the second most attractive mode of transport after cycling, meaning that a DRT service could have a potentially large uptake in the population. Our results could be used by decision makers and service providers for the design of a DRT service.