The problem of transfer learning is considered in the domain of crowd counting. A solution based on Bayesian model adaptation of Gaussian processes is proposed. This is shown to produce intuitive model updates, which are tractable, and lead to an adapted model (predictive distribution) that accounts for all information in both training and adaptation data. The new adaptation procedure achieves significant gains over previous approaches, based on multi-task learning, while requiring much less computation to deploy. This makes it particularly suited for the problem of expanding the capacity of crowd counting camera networks. A large video dataset for the evaluation of adaptation approaches to crowd counting is also introduced. This contains a number of adaptation tasks, involving information transfer across video collected by 1) a single camera under different scene conditions (different times of the day) and 2) video collected from different cameras. Evaluation of the proposed model adaptation procedure in this dataset shows good performance in realistic operating conditions.