Ridesharing services have revolutionized transportation, transforming the manner in which individuals navigate urban environments. The estimation of ride-sharing demand is crucial for enhancing service utilization, reliability, and mitigating traffic congestion. In this research, we employ spatial and spatiotemporal Bayesian models to estimate ride-sharing demand in the 77 Chicago community areas. We investigate various explanatory variables, including demographic, socio-economic, transportation, and land-use features. The Bayesian models adjust for random and structured errors to account for spatial correlations. Additionally, we utilize spatially correlated priors for explanatory variables to improve model precision. Model diagnostics demonstrate the absence of residual spatial structure in the spatial regression, confirming effective management of spatial correlation. The spatiotemporal model yields a squared correlation of 0.95 between observed ride-shares and fitted values, indicating robust predictive power. Demographic factors, including population size and crime rate, emerge as the primary determinants positively influencing ride-sharing demand. Higher income levels, increased numbers of economically active citizens, and higher proportions of car-free households are associated with increased demand. Public transit availability and walkability also play significant roles in ride-sharing patterns in Chicago. Our study demonstrates that ride-sharing demand recovered in 2022 following COVID-19-related closures, particularly during weekends. This research provides planners and policymakers with insights to enhance first and last mile services, identify underserved areas, and enable ride-sharing to address public transportation gaps. Such knowledge has the potential to enhance mobility for individuals with disabilities and those residing in rural areas. This study, utilizing Bayesian models, offers deeper insights into ride-sharing demand, thereby contributing to improved urban transportation planning.