We introduce Bayesian sensing hidden Markov models (BS-HMMs) to represent speech data based on a set of state-dependent basis vectors. By incorporating the prior density of sensing weights, the relevance of a feature vector to different bases is determined by the corresponding precision parameters. The BS-HMM parameters, consisting of the basis vectors, the precision matrices of sensing weights and the precision matrices of reconstruction errors, are jointly estimated by maximizing the likelihood function, which is marginalized over the weight priors. We derive recursive solutions for the three parameters, which are expressed via maximum a posteriori estimates of the sensing weights. Experimental results on an LVCSR task show consistent gains over conventional HMMs with Gaussian mixture models for both ML and discriminative training scenarios.