The compact sizes, lack of available physical protection, and complex maneuvering patterns of motorized two-wheeler (MTW) riders make them more vulnerable to crash risks and accidents. Considering the increased vulnerability of MTWs in dense urban mixed traffic environments, a proper evaluation and modeling of their lateral movement decisions and driving style can enhance safety associated with the riders and augment the reliability of the existing microsimulation models. Utilizing trajectory data of a six-lane divided urban arterial, the current study attempts to investigate the lateral movement (lateral shift) tendency of MTWs, addressing different influential variables that may affect riders’ decisions and describing how this choice is affected by prevailing traffic conditions. Based on several driving style parameters, such as change in speed, change in angular position, and longitudinal gap maintained with rear vehicles, this study further contributes to the existing literature by proposing a new index for identifying the driving style of riders during the lateral shifting process. Modeling results of a multinomial logit model indicated the importance of considering longitudinal and lateral gaps, vehicle speeds, and lateral fluctuations made by the subject MTW in the past trajectories in modeling the lateral shift decisions of riders. Considering the number of lateral fluctuations as an indicator of MTWs’ driving style, a new “aggressiveness index” is defined and, accordingly, a modeling approach is proposed to classify aggressive and non-aggressive driving styles of the riders. The results suggest that the history of past trajectories of the subject MTW during lateral shifting should be considered, and consideration of a non-linear relationship among the parameters can result in a better classification of driving style of MTW riders.