Cat-state　qubits　formed　by　photonic　coherent　states　are　a　promising　candidate　for　realizing　fault-tolerant　quantum　computing.　Such　logic　qubits　have　a　biased　noise　channel　where　the　bit-flip　error　dominates　over　all　the　other　errors.　In　this　manuscript,　we　propose　an　optimally　robust　protocol　using　the　control　method　of　shortcuts　to　adiabaticity　to　realize　a　high-fidelity　state　transfer　in　a　cat-state　qubit.　We　construct　a　shortcut　based　on　the　Lewis-Riesenfeld　invariant　and　examine　the　stability　versus　different　types　of　perturbations　for　the　fast　and　robust　bit　flipping.　Numerical　simulations　demonstrate　that　the　bit　flipping　can　be　robust　against　systematic　errors　in　our　protocol.　Even　when　the　parameter　imperfection　rate　for　bit-flip　control　is　20%,　the　final　population　of　the　target　state　can　still　reach　≥　99%.　The　optimally　robust　control　provides　a　feasible　method　for　fault-tolerant　and　scalable　quantum　computation.　©　2025　Optica　Publishing　Group.