The ability of robots to grasp novel objects has industry applications in e-commerce order fulfillment and home service. Data-driven grasping policies have achieved success in learning general strategies for grasping arbitrary objects. However, these approaches can fail to grasp objects which have complex geometry or are significantly outside of the training distribution. We present a Thompson sampling algorithm that learns to grasp a given object with unknown geometry using online experience. The algorithm leverages learned priors from the Dexterity Network robot grasp planner to guide grasp exploration and provide probabilistic estimates of grasp success for each stable pose of the novel object. We find that seeding the policy with the Dex-Net prior allows it to more efficiently find robust grasps on these objects. Experiments suggest that the best learned policy attains an average total reward 64.5% higher than a greedy baseline and achieves within 5.7% of an oracle baseline when evaluated over 300,000 training runs across a set of 3000 object poses.