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Unmanned aerial vehicles (UAVs) are increasingly employed for numerous public and civil applications, such as goods delivery, medicine, surveillance, and telecommunications. For the latter, UAVs with onboard communication equipment may help temporarily offload traffic onto the neighboring cells in fifth-generation networks and beyond (5G+). In this paper, we propose and evaluate the use of UAVs traveling over the area of interest to relieve congestion in 5G+ systems under spontaneous traffic fluctuations. To this end, we assess two inherently different offloading schemes, named routed and controlled UAV `bridging'. Using the tools of renewal theory and stochastic geometry, we analytically characterize these schemes in terms of the fraction of traffic demand that can be offloaded onto the UAV `bridge' as our parameter of interest. This framework accounts for the unique features of millimeter-wave (mmWave) radio propagation and city deployment types with potential line-of-sight (LoS) link blockage by buildings. We also introduce enhancements to the proposed schemes that significantly improve the offloading gains. Our findings offer evidence that the UAV `bridges' may be used for efficient traffic offloading in various urban scenarios.