Most continual learning (CL) algorithms have focused on tackling the stability-plasticity dilemma, that is, the challenge of preventing the forgetting of past tasks while learning new ones. However, we argue that they have overlooked the impact of knowledge transfer when the training dataset of a certain task is biased — namely, when the dataset contains some spurious correlations that can overly influence the prediction rule of a model. In that case, how would the dataset bias of a certain task affect the prediction rules of a CL model for future or past tasks? In this work, we carefully design systematic experiments using three benchmark datasets to answer the question from our empirical findings. Specifically, we first show through two-task CL experiments that standard CL methods, which are oblivious of the dataset bias, can transfer bias from one task to another, both forward and backward. Moreover, we find out this transfer is exacerbated depending on whether the CL methods focus on stability or plasticity. We then present that the bias is also transferred and even accumulates in longer task sequences. Finally, we offer a standardized experimental setup and a simple, yet strong plug-in baseline method, dubbed as group-class Balanced Greedy Sampling (BGS), which are utilized for the development of more advanced bias-aware CL methods.