The performance of ride-sourcing services such as Uber and Lyft is determined by the collective choices of individual drivers who are not only chauffeurs but private fleet providers. In such a context, ride-sourcing drivers are free to decide whether to accept or decline ride requests assigned by the ride-hailing platform. Drivers’ ride acceptance behaviour can significantly influence system performance in terms of riders’ waiting time (associated with the level of service), drivers’ occupation rate and idle time (related to drivers’ income), and platform revenue and reputation. Hence, it is of great importance to identify the underlying determinants of the ride acceptance behaviour of drivers. To this end, we collected a unique dataset from ride-sourcing drivers working in the United States and the Netherlands through a cross-sectional stated preference experiment designed based upon disparate information conveyed to the respondents. Using a choice modelling approach, we estimated the effects of various existing and hypothetical attributes influencing the ride acceptance choice. Employment status, experience level with the platform, and working shift are found to be the key individual-specific determinants. Part-time and beginning drivers who work on midweek days (Monday-Thursday) have a higher tendency to accept ride offers. Results also reveal that pickup time, which is the travel time between the driver’s location and the rider’s waiting spot, has a negative impact on ride acceptance. Moreover, the findings suggest that a guaranteed tip (i.e., the minimum amount of tip that is indicated upfront by the prospective rider, a feature that is currently not available) and an additional income due to surge pricing are valued noticeably higher than trip fare. The provided insights can be used to develop customised matching and pricing strategies to improve system efficiency. Since the study has been conducted during the COVID-19 crisis, the potential implications of the pandemic on ride acceptance behaviour have been examined using an Integrated Choice and Latent Variable (ICLV) model. The results show that drivers with a higher sensitivity to the COVID-19 effects tend to have a lower acceptance rate.