In cell-free massive multiple-input multiple-output (MIMO) systems, the beamforming strategies at the base stations (BSs) and user equipments (UEs) can be computed building on bi-directional training. However, the precoding/decoding optimization in the downlink (DL) and in the uplink (UL) generally requires two separate bi-directional training phases, which can be wasteful in the case of short scheduling blocks. This paper proposes a framework to reduce the bi-directional training overhead by considering a common beamforming training strategy for both DL and UL when the UEs to be served in the two directions are the same. In doing so, we consider the problem of maximizing the (weighted) minimum DL-UL rate among all the UEs. Numerical results show that, in scenarios with short scheduling blocks, the proposed framework outperforms the case where the DL and UL beamforming strategies are computed individually via two separate bi-directional training phases thanks to the reduced training overhead. Even more substantial gains are observed with respect to the case with a single bi-directional training phase, where the DL (resp. UL) beamforming strategies are reused in the UL (resp. DL).