The implementation of bike-sharing systems (BSSs) is expected to lead to modifications in the travel habits of transport users, one of which is the choice of travel mode. Therefore, this research focuses on the identification of factors influencing the shift of private car users to BSSs based on stated preference survey data from the city of Alexandroupolis, Greece. A binary logit model is employed for this purpose. The estimation results indicate the impacts of gender, income, travel time, travel cost and safety-related aspects on the mode shift, through which behavioural insights are derived. For example, car users are found to be twice as sensitive to the cost of BSSs than to that of car. Similarly, they are highly sensitive to BSS travel time. Based on the behavioural findings, policy measures are suggested under the following categories: (i) finance, (ii) regulation, (iii) infrastructure, (iv) campaigns and (v) customer targeting. In addition, a secondary objective of this research is to obtain insights from the comparison of the specified logit model with a machine learning approach, as the latter is slowly gaining prominence in the field of transport. For the comparison, a random forest classifier is also developed. This comparison shows a coherence between the two approaches, although a discrepancy in the feature importance for gender and travel time is observed. A deeper exploration of this discrepancy highlights the hurdles that often occur when using mathematically more powerful models, such as the random forest classifier.