Assuming a bidirectional relay assisted network, we study the problem of optimal resource sharing between two transceiver pairs. One pair, referred to as the primary pair, is considered to be the owner of the spectral resources. The rates of the two transceivers in this pair must be guaranteed to be greater than a predefined threshold. The second pair, called the secondary pair, is assumed to own the relay infrastructure. The secondary network allows the primary pair to use the relays to establish a bidirectional communication between its transceivers. In exchange for this cooperation, the primary pair assigns a portion of its resources to the secondary pair, thereby enabling a two-way communication between the secondary transceivers. Assuming amplify-and-forward relaying scheme, the relays collectively build two network beamformers each of which enables communication between the two transceivers in one pair. Aiming to optimally calculate the parameters of the two networks, we study three different design problems. The first approach relies on maximizing the smaller of the secondary transceiver rates subject to two separate constraints on the total power levels consumed in the primary and the secondary networks while providing a minimum data rate to the primary pair. In the second approach, we consider a constraint on the average total power consumed in both networks, while maximizing the smaller of the secondary transceiver rates. The third approach extends the second method to materialize a spectrum leasing and sharing scheme for the case when the primary network is active with a certain probability.