In this work, the dynamics of a self-propelled stochastic particle under the influence of an axisymmetric light field was experimentally studied. The particle under consideration has the main characteristic of carrying a light sensor in an eccentric location. For the chosen experimental conditions, the emerging trajectories were orbital, and, more interestingly, they presented two preferential radial distances. A mathematical model incorporating the key experimental components was introduced. By means of numerical simulations and theoretical analysis, it was found that, in addition to the orbiting behavior, the sensor location could produce trapped or diffusive behaviors. Furthermore, the study revealed that stochastic perturbation and the eccentric location of the sensor are responsible for inducing bistability in the orbital trajectories, in agreement with the experimental observations.