The COVID-19 pandemic and its related events (e.g., lockdown policies, vaccine distributions) have caused disruptive changes in travel patterns and urban mobility services. Cities need to understand the impacts of these factors on mobility activities for taking effective actions to restore/reform urban transportation systems and prepare for future shocks. In this study, we investigate the correlations between the COVID-19 related factors and the usage of on-demand mobility services (OMS, i.e., street-hailing, ride-hailing, and bike-sharing) through a two-step framework. In the first step, we construct lowdimensional representations, called mobility signals, of multivariate mobility data which provide a temporal understanding of the variation of trips across different modes. Then the Bayesian structural time series model is utilized to estimate the regression coefficients and inclusion probability of different time-varying factors including COVID-19 cases, policies, and vaccination rates in predicting each mobility signal. This framework is adopted in New York City (NYC) and Chicago, two example cities that have been significant affected by COVID-19 disruptions and that have comprehensive on-demand mobility services. The results suggest an asymmetrical influence of COVID-19 related policies to the usage of OMS: the mobility/ business restrictions can trigger fast and consistent decrease of ridership, but lifting these restrictions does not result in a fast rebound. Our analyses further uncovers the heterogeneity of spatial impacts of different COVID-19 related policies. A one-year prediction of OMS usage is conducted and the results suggest a highly uncertain future of the ride-hailing and street-hailing services, and relatively stable bike-sharing usage in the near future.