In the production and operation, inherent variability and uncertainty necessitate addressing unit-to-unit heterogeneity in initial performance values and degradation processes. This article presents a bi-stochastic exponential dispersion process (BS-ED) designed to account for heterogeneity in both initial performance values and degradation processes. First, based on the ED process, the time and acceleration covariates are introduced to form a nonlinear accelerated ED process, and a random effect coefficient associated with the accelerated stress is incorporated to consider the heterogeneity of the process. Meanwhile, through the modelling of degradation time-shift, a degradation model considering the stochastic initial value of the product performance is developed. To effectively conduct the statistic inference of the BS-ED process, an improved stochastic EM algorithm is proposed, and the information matrix and Ito calculus are combined to estimate the confidence intervals. Finally, the stability of the method is verified by simulation and analyzed by two real cases.