At the brink of the introduction of self-driving vehicles, only little is known about how potential users perceive them. This is especially true for self-driving vehicles deployed in public transport services. In this study, the relative preferences for a trip with a self-driving bus is assessed compared to a trip with a regular bus, based on a stated preference experiment. Based on the responses of 282 respondents from the Netherlands and Germany, a discrete choice model is estimated as a Mixed Logit model including attitudes towards trust in self-driving vehicles and interest in technology. The results show that currently public transport passengers prefer the self-driving bus over the regular bus only for short trips. This is due to the finding that the value of travel time is about twice as high for the self-driving bus as for the regular bus for a short commuting trip. Findings from this study further suggest that the popularity of self-driving busses decreases with the presence of a human steward on-board, or if they are operated as a demand-responsive service with fixed routes. People who currently show a strong interest in technology or trust in automated vehicle technology perceive the self-driving busses better than others. The trust-effect is especially strong for women. In general, men are found to be more inclined to choose the self-driving bus than women. Preferences towards automated public transport services are expected to evolve along with the transition from demonstration pilots to their deployment in regular operations.