Bedload transport often exhibits dual-mode behavior due to interactions of spatiotemporal controlling factors with the migrating three-dimensional bedforms (characterized by the fully developed patterns in the bed, such as alternate bars, pools, and clusters). This study explores dual-mode bedload transport based on experimental measurements and develops Einstein's exponential-based model to characterize large fluctuations of bedload sediment discharge. The particle waiting time, particle flux, and bed elevation are measured in a series of well-controlled laboratory experiments. Flume experiments show that the waiting time distribution of sediments gives a bimodal characteristic, two distinct modes can be identified from the measured data. This study encapsulates this dual-mode bedload transport behavior in a hyperexponential distribution of sediment resting times and introduces it into the continuous time random walk (CTRW) framework. Considering the scaling limit of the thin/heavy-tailed CTRW processes, a single-rate mass transfer (SRMT) and fractional-derivative SRMT (F-SRMT) models are obtained, and the model parameters are determined from the hyperexponential distribution. Further analyses reveal that the dual-mode bedload transport behavior is controlled by mass exchange between the mobile and immobile zones, and a dimensionless index eta can quantify the intensity of dual-mode behavior. Applications show that the dual-mode bedload transport models are much more accurate in characterizing bedload transport in a mixed-size gravel bed than the traditional exponential-based model, and the nonlocal movement of bedload sediments is significant in the mixed-size gravel bed. Further investigations will focus on the applicability test of the dual-mode models to other flow regimes and conditions.