This article develops a self-triggered prescribed-time (PT) smooth bipartite formation tracking control (BFTC) strategy for uncertain nonlinear multiagent systems (NMASs) operating over directed graphs. An adaptive backstepping framework is employed for formation control design. To enhance the applicability of distributed protocols, we investigate practical BFTC for multiagent systems (MASs) with followers that are subject to unknown nonlinear dynamics, external disturbances, and actuator faults within cooperative-competitive interaction topologies. Radial basis function neural networks (RBFNNs) are employed to approximate these uncertainties, leveraging their universal approximation capability and localized response characteristics. Importantly, in contrast to previous studies, this work achieves user-defined tracking performance suitable for practical NMAS implementations. The proposed bipartite formation tracking controller guarantees compliance with the user-specified settling time without reliance on initial conditions. Furthermore, considering the constraints imposed by limited communication bandwidth, a distributed dynamic self-triggered control (DSTC) mechanism is developed to enhance transmission efficiency. Unlike traditional strategies, the proposed DSTC dynamically adjusts triggering intervals based on bipartite formation tracking errors (BFTEs). This adaptability facilitates a real-time balance between communication load and system performance. Simulation results validate the efficacy of the proposed control strategy.