This paper considers the problem of learning the parameters of a Bayesian Network, assuming the structure of the network is given, from a privacy-sensitive dataset that is distributed between multiple parties. For a binary-valued dataset, we show that the count information required to estimate the conditional probabilities in a Bayesian network can be obtained as a solution to a set of linear equations involving some inner product between the relevant different feature vectors. We consider a random projection-based method that was proposed elsewhere to securely compute the inner product (with a modified implementation of that method).