Open human mobility data is considered an essential basis for the profound research and analysis required for the transition to sustainable mobility and sustainable urban planning. Cycling data has especially been the focus of data collection endeavors in recent years. Although privacy risks regarding location data are widely known, practitioners often refrain from advanced privacy mechanisms to prevent utility losses. Removing user identifiers from trips is thereby deemed a major privacy gain, as it supposedly prevents linking single trips to obtain entire movement patterns. In this paper, we propose a novel attack to reconstruct user identifiers in GPS trip datasets consisting of single trips, unlike previous ones that are dedicated to evaluating trajectory-user linking in the context of check-in data. We evaluate the remaining privacy risk for users in such datasets and our empirical findings from two real-world datasets show that the risk of re-identification is significant even when personal identifiers have been removed, and that truncation as a simple additional privacy mechanism may not be effective in protecting user privacy. Further investigations indicate that users who frequently visit locations that are only visited by a small number of others, tend to be more vulnerable to re-identification.