High-fidelity generation of entangled states is a central task in quantum information processing. In this work, we propose an all-optical analytical and robust scheme for generating two-excitation Bell states in a two-atom system with dipole-dipole interaction. Owing to the interaction-induced splitting of the collective single-excitation states, the relevant dynamics can be restricted to a cascade-type three-state subspace under frequency-selective resonant optical driving. By applying the Morris-Shore (MS) transformation, the original three-state dynamics is decomposed into an effective two-state bright subspace and a decoupled dark state, which provides a transparent physical picture for the state-preparation process. Based on this reduced description, the pulse-area conditions required for deterministic generation of the target Bell states are obtained analytically. Numerical simulations confirm the validity of these analytical conditions and show that different pulse-area conditions can all lead to high-fidelity Bell-state generation. However, they correspond to distinct dynamical pathways and different degrees of intermediate-state participation. In particular, the pathway with weaker intermediate-state population exhibits better intrinsic tolerance to pulse-area deviations, whereas the pathway involving stronger cascade transfer is more sensitive to such errors. To further suppress control imperfections, we introduce a composite pulse-pair scheme by mapping the robust preparation problem in the original three-state system onto a robust rotation problem in the MS bright subspace. The results show that the composite pulse-pair scheme can significantly broaden the high-fidelity error-tolerance window compared with the single pulse-pair scheme, while preserving the intrinsic robustness difference between different dynamical pathways. This scheme therefore combines analytical controllability with enhanced resistance to systematic pulse-area errors. The present study provides an error-resilient route for the all-optical generation of two-excitation Bell states and may offer useful theoretical guidance for future experimental implementations in interacting neutral-atom systems and other optically controllable quantum platforms.