The bilayer skyrmion composed of upper and lower tightly coupled skyrmions on two layers with completely compensated topological charges (called as anti-topology here), has become one feasible improvement of conventional skyrmion to realize straight motion without skyrmion Hall effect, which has aroused great interest in practical applications. The present work investigates a general model (without external magnetic field) for the frustration-induced anti-topological bilayer magnetic textures with rich morphologies, and discusses the modulations of key parameters on the energy barrier and the current-driven dynamics. It is revealed that the interlayer coupling plays a key role in preventing distortion, and thus helps to reach a faster velocity. This model can be realized in various frustrated magnetic materials with antiferromagnetically coupled bilayer, providing a helpful guidance for the material design and application of topological magnetic textures.