One challenge in delay tolerant networks (DTNs) is efficient routing, as the lack of contemporaneous end-to-end paths makes conventional routing schemes inapplicable. Many existing DTN routing protocols adopt multi-copy replication and/or are incognizant of mobility models. Hence they are not suitable for networks with extremely stringent resources and time-varying mobility models such as underwater sensor networks. In this paper, we propose a generic prediction assisted single-copy routing (PASR) scheme that can be instantiated for different mobility models in underwater sensor networks. PASR employs an effective greedy algorithm which captures the features of network mobility patterns, and provides guidance on how to use historical information. We demonstrate the superior performance of PASR through simulation.