Bistable perception is a fascinating psychological phenomenon in which the conscious perception that a person experiences for a single image spontaneously changes across time. In our experiment, twelve participants observed a dynamic display of moving dots, which appeared to rotate in one direction before seeming to reverse. The study consisted of six sessions, and during each session, participants observed sequences of these moving dots across five one-minute blocks. They were instructed to report any perceived changes in the rotation’s direction – specifying shifts to the left, to the right, or expressing that the direction has become uncertain. Each report of perceived directional change, along with the time taken to notice such a change, was recorded. This process yielded a detailed dataset of response patterns and the timing of perceptual switches. We developed two models to account for the results: a quantum walk versus a Markov random walk model, both with reflecting bounds and measurement operators designed to detect the three responses. Both models required fitting 6 parameters to each session (5 min of viewing) using maximum likelihood methods, and then we computed a \(G^2\) lack of fit measure for each model, person, and session. The results, averaged across the 6 sessions for each participant, indicated that the quantum model produced a better fit for 9 out of the 12 participants as compared to the Markov model.