In many real-world transportation systems, passengers are often required to make a number of interchanges between different modes of transport. As cities continue to grow, a greater number of these connections tend to occur within centrally located Transport Hubs. In order to encourage the uptake of public transport in major cities, it is important for passengers to be able to connect between travel modes efficiently; thus it is desirable from a transport planning perspective to improve the synchronisation of connecting services at a Transport Hub. In this paper we consider the problem of designing shuttle-bus routes for passengers intending to connect with one of four different modes of transport at a Transport Hub; in such a way so as to minimise the total travel time and the missed connection costs, whilst incorporating time-of-day effects and passenger heterogeneity with respect to value-of-time. This problem is modelled as a capacitated Dial-a-Ride problem with time windows and solved via column generation and an efficient label setting algorithm. We compare the results of our approach with that of a classical Dial-a-Ride problem on 40 datasets reflecting different time-of-day passenger requests. Results indicate that our approach has the potential to achieve an average 48% improvement in total cost over the classical approach.