The lack of emergency medical transportation is viewed as the main barrier to the access and availability of emergency medical care in low- and middle-income countries (LMICs). In this paper, we present a robust optimization approach to optimize both the location and routing of emergency response vehicles, accounting for uncertainty in travel times and spatial demand characteristic of LMICs. We traveled to Dhaka, Bangladesh, the sixth largest and third most densely populated city in the world, to conduct field research resulting in the collection of two unique data sets that inform our approach. These data are leveraged to estimate demand for emergency medical services in an LMIC setting and to predict the travel time between any two locations in the road network for different times of day and days of the week. We combine our prediction-optimization framework with a simulation model and real data to provide an in-depth investigation into three policy-related questions. First, we demonstrate that outpost locations optimized for weekday rush hour lead to good performance for all times of day and days of the week. Second, we find that the performance of the current system could be replicated using one third of the current outpost locations and one half of the current number of ambulances. Finally, we show that a fleet of small ambulances has the potential to significantly outperform traditional ambulance vans. In particular, they are able to capture approximately three times more demand while reducing the median average response time by roughly 10%-18% over the entire week and 24%-35% during rush hour because of increased routing flexibility offered by more nimble vehicles on a larger road network. Our results provide practical insights for emergency response optimization that can be leveraged by hospital-based and private ambulance providers in Dhaka and other urban centers in developing countries.