Fundamental requirements in mobility are time, cost and comfort. Individual car ownership satisfies comfort component and to some extent, the time component as well. However, owning and maintaining a car is prohibitive for many due to cost and convenience implications. In selecting other public modes of transportation, a taxi or rental car would provide a more comfortable ride with little to none waiting time and conforms to the passengers mobility requirements. However, the cost is too high and cannot be sustained as a regular mode of transport. On the other hand, shared public transport such as bus or train is more affordable but requires the passenger to conform their schedule to a set timetable that operates no matter the changes in demand. In developing countries, however, the shared public transport alternatives do not have timetables and waiting time could be up to an hour. Recent research in shared mobility systems, specifically Demand Responsive Transport (DRT), addresses this situation. Solutions to DRT trip scheduling are constrained to the variation of DRT specifications but does not vehicle schedule and quorum specifications considerations. We aim to reduce passenger waiting time for shared mobility and propose a design of a DRT-based Demand Responsive MaaS (Mobility as a Service) model that provides centralized management and ICT support. Our design adds time constraints of vehicle schedule to the DRT problem. We propose a trip scheduling and cost sharing algorithm for our designed model and base our approach on a DRT heuristic algorithm and a quorum to enforce a minimum demand. A simulation experiment showed average waiting time reduced by 44.4% compared to other DRT time optimization solutions. We conducted a pilot study in Dhaka, Bangladesh for 4 months. Actual average waiting time reduced to 25% compared to current public transport in Dhaka.