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Pulsed arterial spin labeling (PASL) techniques potentially allow the absolute, noninvasive quantification of brain perfusion using MRI. This can be achieved by fitting a kinetic model to the data acquired at a number of sampling times. However, the intrinsically low signal-to-noise ratio of PASL measurements usually requires substantial signal averaging, which may result in undesirably long scanning times. A judicious choice of the sampling points is, therefore, crucial in order to minimize scanning time, while optimizing estimation accuracy. On the other hand, a priori information regarding the model parameters may improve estimation performance. Here, we propose a Bayesian framework to determine an optimal sampling strategy and estimation method for the measurement of brain perfusion and arterial transit time (ATT). A Bayesian Fisher information criterion is used to determine the optimal sampling points and a MAP criterion is employed for the estimation of the model parameters, both taking into account the uncertainty in the model parameters as well as the amount of noise in the data. By Monte Carlo simulations, we show that using optimal compared to uniform sampling strategies, as well as the Bayesian estimator relative to a standard least squares approach, improves the accuracy of perfusion and ATT measurements. Moreover, we also demonstrate the applicability of the proposed approach to real data, with the advantage of reduced intersubject variability relative to conventional sampling and estimation approaches.