We report on low-power optical bistability in a vertical cavity structure at 1.55-mu m wavelength due to the bandgap resonant dispersive optical nonlinearity of InGaAsP, In this structure, a GaAs-AlAs Bragg reflector grown on GaAs and the nonlinear medium grown on InP are bonded through waferfusion, leading to a high-quality vertical cavity after deposition of a top dielectric mirror. This device shows interesting characteristics for optical switching applications at fiber communication wavelengths, such as a switching contrast higher than 8:1 in the reflective mode and a bistability threshold power as low as 0.6 mW. True steady-state memory effect is observed with continuous-wave input, and the device switching time is in the ns range.