Bike-sharing systems allow occasional and regular users to move by replacing other transport modes for the same trip or generating a new journey. Our research assesses the demand for Lisbon’s public dock-based bike-sharing system (BSS) users named after GIRA. This paper aims to identify the determinant factors that influence the potential of the BSS to generate new trips or replace previous modes using a binary logit model based on a survey of 3112 BSS users. The survey results indicate that GIRA generated approximately 20% of the BSS trips, i.e., they would not have been realized if GIRA did not exist. The remaining BSS trips replaced other motorized (55%) and non-motorized (25%) trips. The main determinants explaining a higher likelihood of replacing other modes are having a yearly GIRA pass and a bike-sharing station within a 5-min walking distance. In contrast, regular car users are more likely to generate new trips, suggesting they use bike-sharing for recreational purposes. The findings provide policymakers with an assessment of the determinants that can influence bike-sharing users to generate or substitute trips from other modes for bike-sharing and, consequently, give policies to potentially increase bike-sharing mobility share.