Mobility strategies for wireless sensor networks (WSNs) are presented. We introduce a grazing mobility strategy for mobile WSNs, inspired by the foraging behaviour of herbivores grazing pastures. We present Bayesian network GRAZing (BNGRAZ) that implements the proposed WSN grazing strategy. BNGRAZ uses local neighbourhood information to predict coverage and connectivity performance changes related to sensor node motion characteristics. This enables a sensor node to predict the performance implications related to its direction of movement. We implement the BNGRAZ approach to grazing in a custom built mobile WSN simulator. The WSN performance criteria considered during the validation process include coverage, redundancy, connectivity, and network lifetime.