Bus transportation is considered as one of the most convenient and cheapest modes of public transportation in Indian cities. Due to their cost-effectiveness and wide reachability, they help a significant portion of the human population in cities to reach their destinations every day. Although from a transportation point of view they have numerous advantages over other modes of public transportation, they also pose a serious threat of contagious diseases spreading throughout the city. The presence of numerous local spatial constraints makes the process and extent of epidemic spreading extremely difficult to predict. Also, majority of the studies have focused on the contagion processes on scale-free network topologies whereas, spatially-constrained real-world networks such as, bus networks exhibit a wide-spectrum of network topology. Therefore, we aim in this study to understand this complex dynamical process of epidemic outbreak and information diffusion on the bus networks for six different Indian cities using SI and SIR models. This will allow us to identify epidemic thresholds for these networks which will help us in controlling outbreaks by developing node-based immunization techniques.