An important step in systems biology is to improve our knowledge of how genes causally interact with one another. A few approaches have been proposed for the estimation of causal effects among genes, either based on observational data alone or requiring a very precise intervention design with one knock-out experiment for each gene. We recently suggested a more flexible algorithm, using a Markov chain Monte Carlo algorithm and the Mallows ranking model, that can analyze any intervention design, including partial or multiple knock-outs, using the framework of Gaussian Bayesian networks. We previously demonstrated the superior performance of this algorithm in comparison to alternative methods, although it can be computationally expensive to implement. The aim of this paper is to propose an alternative approach taking advantage of node pair ordering preferences to sample the posterior distribution according to the Babington-Smith ranking distribution. This novel algorithm proved, both in a simulation study and on the DREAM4 challenge data, to attain estimation of the causal effects as accurate as the MCMC-Mallows approach with a highly improved computational efficiency, being at least 100 times faster. We also tested our algorithm on the Rosetta Compendium dataset with more contrasted results. We nevertheless anticipate that our new approach might be very useful for practical biological applications.