The paper concerns estimation of the rose of directions of a stationary fibre process in $R^3$ from the intersection counts of the process with test planes. A new approach is suggested based on Bayesian statistical techniques. The method is derived from the special case of a Poisson line process however the estimator is shown to be consistent generally. Markov chain Monte Carlo (MCMC) algorithms are used for the approximation of the posterior distribution. Uniform ergodicity of the algorithms used is shown. Properties of the estimation method are studied both theoretically and by simulation.