We report broadband spectroscopy and numerical analysis by which we explore propagating spin waves in a magnetic bilayer consisting of a 23-nm thick permalloy film deposited on 130-nm thick Y_3Fe_5O_12. In the bilayer, we observe a characteristic mode that exhibits a considerably larger group velocity at a small in-plane magnetic field than both the magnetostatic and perpendicular standing spin waves. Using the finite element method, we confirm the observations by simulating the mode profiles and dispersion relations. They illustrate the hybridization of spin-wave modes due to exchange coupling at the interface. The high-speed propagating mode found in the bilayer can be utilized to configure multifrequency spin-wave channels enhancing the performance of spin-wave-based logic devices.