A Bayesian simulation-based method is developed for estimating a class of interest rate models known as Affine Term Structure (ATS) models. The technique is based on a Markov Chain Monte Carlo algorithm, with the discrete observations on yields augmented by additional higher frequency latent data. The introduction of augmented yield data reduces the bias associated with estimating a continuous time process using an approximate discrete time model. The technique is demonstrated using a singlefactor term structure model which possesses closed form solutions for the transition densities. Numerical application of the method is demonstrated using simulated data. The results show that increasing the degree of augmentation in the yield curves does, overall, produce estimates that more closely reflect those based on the use of the exact transition functions. However, the results also indicate that the benefits of increasing the degree of augmentation may, to some extent, be offset by the increased uncertainty in estimation associated with the introduction of additional highly correlated latent yields.