This thesis developed four mathematical models using continuum approximation and applied them to an urban bus route. Alternative operating strategies are compared to conventional all-stop operations. The comparison of skip-stop and express-local schemes with stop skipping designs and on-demand strategies with flexible stopping patterns are conducted to determine the most efficient bus operating service under various conditions. Each alternative has a total cost that includes walking time, waiting time, in-vehicle travel time, and transferring between lines, in addition to operating costs. This thesis also considers the impact of the COVID-19 pandemic on public transit. As a result, we incorporated the crowding disutility based on the loading factor and the denied boarding costs into the optimization models. First, we solved the theoretical case and determined the most efficient bus operating strategy for various ranges of passenger demand and average trip length. Next, we solved the continuous optimization models by optimizing bus headway and stop spacing. Additionally, this thesis conducted sensitivity analyses of various conditions, including determining the most efficient strategy under fleet size constraints as well as the sensitivity of passengers to crowding and travel times using numerical examples. The solution proposed in this thesis is responsive to changes in demand, trip patterns, and passenger sensitivity to cost components. The model is applied to a bus route in Calgary, Canada, and provides an optimal bus dispatching scheme for two scenarios, with and without considering crowding discomfort. Results show that on-demand services have the lowest generalized costs in scenarios with low demand. In the case of higher demand and longer trips, conventional all-stop systems are preferred. Under high demand and longer passenger trips, skip-stop and express-local services can lower overall system costs. Considering crowding measures, the lowest cost alternative option shifts from conventional services to strategies with stop-skipping designs, such as skip-stop and express-local policies. Express-local strategy dominates other services when the fleet size is limited, and crowding is considered.