In operational modal analysis, the modal parameters (natural frequencies, damping ratios and mode shapes), obtained with stochastic subspace identification from ambient vibration measurements of structures, are subject to statistical uncertainty. It is hence necessary to evaluate the uncertainty bounds of the obtained results, which can be done by a first-order perturbation analysis. To obtain vibration measurements at many coordinates of a structure with only a few sensors, it is common practice to use multiple sensor setups for the measurements. Recently, a multi-setup subspace identification algorithm has been proposed that merges the data from different setups prior to the identification step to obtain one set of global modal parameters, taking the possibly different ambient excitation characteristics between the measurements into account. In this paper, an algorithm is proposed that efficiently estimates the covariances on modal parameters obtained from this multi-setup subspace identification. The new algorithm is validated on multi-setup ambient vibration data of the Z24 Bridge, benchmark of the COST F3 European network.