Estimating spectral reflectance has attracted extensive research efforts in color science and machine learning, motivated through a wide range of applications. In many practical situations, prior knowledge is available that ought to be used. Here, we have developed a general Bayesian method that allows the incorporation of prior knowledge from previous monochromator and spectrophotometer measurements. The approach yields analytical expressions for fast and efficient estimation of spectral reflectance. In addition to point estimates, probability distributions are also obtained, which completely characterize the uncertainty associated with the reconstructed spectrum. We demonstrate that, through the incorporation of prior knowledge, our approach yields improved reconstruction results compared with methods that resort to training data only. Our method is particularly useful when the spectral reflectance to be recovered resides beyond the scope of the training data.