Pedestrian routing choices play a crucial role in shaping collective crowd dynamics, yet the influence of interactions among unfamiliar individuals remains poorly understood. In this study, we analyze real-world pedestrian behavior at a route split within a busy train station using high-resolution trajectory data collected over a three-year time frame. We disclose a striking tendency for individuals to follow the same path as the person directly in front of them, even in the absence of social ties and even when such a choice leads to a longer travel time. This tendency leads to bursty dynamics, where sequences of pedestrians make identical decisions in succession, leading to strong patterns in collective movement. We employ a stochastic model that includes route costs, randomness, and social imitation to accurately reproduce the observed behavior, highlighting that local imitation behavior is the dominant driver of collective routing choices. These findings highlight how brief, low-level interactions between strangers can scale up to influence large-scale pedestrian movement, with strong implications for crowd management, urban design, and the broader understanding of social behavior in public spaces.