This paper investigates anti-bump switched linear parameter-varying (sLPV) control for morphing aircraft subject to delayed scheduling variables arising from lagging measurements of structural deformation. Depending on whether the operating mode is correctly detected, scheduling delays are treated as control disturbances or asynchronous switching. Persistent dwell-time switching is introduced to capture both slow transitions during steady flight and rapid transitions during morphing. Using mode-dependent Lyapunov functions and a smooth transition function, stability conditions are established and an anti-bump sLPV controller is designed to accommodate delayed scheduling. Unlike approaches that neglect mode-detection delays, the proposed method explicitly addresses incorrect mode identification during controller switching. Numerical simulations involving a variable-sweep-wing aircraft and an aircraft with a variable wingspan demonstrate the effectiveness of the proposed control framework.