The recent literature on online learning to rank (LTR) has established the utility of prior knowledge to Bayesian ranking bandit algorithms. However, a major limitation of existing work is the requirement for the prior used by the algorithm to match the true prior.In this paper, we propose and analyze adaptive algorithms that address this issue and additionally extend these results to the linear and generalized linear models. We also consider scalar relevance feedback on top of click feedback.Moreover, we demonstrate the efficacy of our algorithms using both synthetic and real-world experiments.