We experimentally demonstrate that the transmission of microwave electromagnetic fields through a bilayer metasurface (BMS) composed of thin conductive rods can abruptly change in a narrow frequency range. A theoretical analysis based on the coupled oscillator model is performed to reveal the physical mechanism behind the frequency-dependent properties of such a structure. Two conditions primarily facilitate the observed high dispersion in the BMS. The first one is the resonant interaction between the incident microwaves and rods, leading to the formation of surface standing waves. These waves with radial electric fields enable the coupling of the near-field of rods in structural layers. The second condition is the complex value of the coupling coefficient between rods of different owing to the delayed interaction process between them. The electromagnetic response here can be effectively controlled by varying the distance between layers and the dielectric properties of the interlayer medium.