Investigations of Raman spectra and surface enhanced Raman spectra (SERS) of supported and suspended bilayer graphene were realized. The ability of SERS to greatly enhance the Raman signals is regarded as useful tools, but the dopants induced by the metallic nanoparticles deposition may affect the electron scattering processes. The four 2D sub-bands of bilayer graphene are associated with four-step Stokes-Stokes double-resonance Raman electron scattering processes and can be analyzed by fitting the corresponding Raman peak with muti-Lorentzian functions. To extricate the dopant effect of the substrate from one of metallic nanoparticles, the suspended graphene is adopted here. The enhancements of SERS over Raman spectra are also calculated. For the supported graphene, the SERS enhancement factors of the sub-bands obey 2D22<2D11<2D21<2D12 and exhibit an integrated intensity that is proportional to the Raman cross-section. For suspended graphene, such factors obey 2D11<2D12<2D21<2D22, with 2D12, 2D21, and 2D22 being close to each other because the rate of the scattering for some processes decrease and contribute to another process in the integrated area of Raman signals when the decays happen. The reason responsible for the factor difference is discussed through the presented analysis of the Raman and SERS signals of supported and suspended bilayer graphene