In reinforcement learning, offline value function learning is the procedure of using an offline dataset to estimate the expected discounted return from each state when taking actions according to a fixed target policy. The stability of this procedure, i.e., whether it converges to its fixed-point, critically depends on the representations of the state-action pairs. Poorly learned representations can make value function learning unstable, or even divergent. Therefore, it is critical to stabilize value function learning by explicitly shaping the state-action representations. Recently, the class of bisimulation-based algorithms have shown promise in shaping representations for control. However, it is still unclear if this class of methods can \emph{stabilize} value function learning. In this work, we investigate this question and answer it affirmatively. We introduce a bisimulation-based algorithm called kernel representations for offline policy evaluation (\textsc{krope}). \textsc{krope} uses a kernel to shape state-action representations such that state-action pairs that have similar immediate rewards and lead to similar next state-action pairs under the target policy also have similar representations. We show that \textsc{krope}: 1) learns stable representations and 2) leads to lower value error than baselines. Our analysis provides new theoretical insight into the stability properties of bisimulation-based methods and suggests that practitioners can use these methods to improve the stability and accuracy of offline evaluation of reinforcement learning agents.