This study delves into the capabilities of reconfig- urable intelligent surfaces (RISs) in enhancing bidirectional non- orthogonal multiple access (NOMA) networks. The proposed approach partitions RIS to optimize the channel conditions for NOMA users, improving NOMA gain and eliminating the re- quirement for uplink (UL) power control. The proposed approach is rigorously evaluated under four practical operational regimes; 1) Quality-of-Service (QoS) sufficient regime, 2) RIS and power efficient regime, 3) max-min fair regime, and 4) maximum throughput regime, each subject to both UL and downlink (DL) QoS constraints. By leveraging decoupled nature of RIS portions and base station (BS) transmit power, closed-form solutions are derived to demonstrate how optimal RIS partitioning can meet UL-QoS requirements while optimal BS power control can ensure DL-QoS compliance. Our analytical findings are validated through simulations, highlighting the significant benefits that RISs can bring to the NOMA networks in the aforementioned operational scenarios.