To improve their interfacial properties, 3D orthogonal woven fabrics with basalt filament yarns were modified with functionalized carboxylated carbon nanotubes (KH570-MWCNTs) and polydopamine (PDA). Fourier infrared spectroscopy (FT-IR) analysis and scanning electron microscopy (SEM) testing were used. It was demonstrated that both methods could successfully modify basalt fiber (BF) 3D woven fabrics. The 3D orthogonal woven composites (3DOWC) were produced with epoxy resin and 3D orthogonal woven fabrics as raw material by the VARTM molding process. The bending properties of the 3DOWC were tested and analyzed by experimental and finite element analysis methods. The results showed that the bending properties of the 3DOWC modified by KH570-MWCNTs and PDA were significantly improved, and the maximum bending loads were increased by 31.5% and 31.0%. The findings of the finite element simulation and the experiment results were in good agreement, and the simulation error value was 3.37%. The correctness of the finite element simulation results and the model’s validity further reveal the material’s damage situation and damage mechanism in the bending process.