Some of the most effective influential spreader detection algorithms are unstable to small perturbations of the network structure. Inspired by bagging in Machine Learning, we propose the first Perturb and Combine (P&C) procedure for networks. It (1) creates many perturbed versions of a given graph, (2) applies a node scoring function separately to each graph, and (3) combines the results. Experiments conducted on real-world networks of various sizes with the k-core, generalized k-core, and PageRank algorithms reveal that P&C brings substantial improvements. Moreover, this performance boost can be obtained at almost no extra cost through parallelization. Finally, a bias-variance analysis suggests that P&C works mainly by reducing bias, and that therefore, it should be capable of improving the performance of all vertex scoring functions, including stable ones.