Fluorination of graphene opens up a bandgap, which creates opportunities for optoelectronics, and also paves the way for the creation of extremely thin insulating layers, which can be important for applications in devices. However, in spite of many interesting features offered by, for example, unequally doped layers in multilayered systems, most of the work has concerned the fluorination of graphene monolayers. Here, the fluorination process of graphene bilayers is investigated through high-resolution Raman mapping followed by analysis of more than 10,000 spectra of bilayer graphene. Isotopically labeled bilayers are used, allowing each individual layer in bilayer graphene to be addressed unambiguously. The fluorinated graphene is prepared through exposure to XeF2. Monolayer graphene is found to be significantly more sensitive to fluorination than bilayer graphene. Through comparison of the D/G area ratio and the position of the G band for turbostratic and Bernal stacked (AB) bilayers, it is found that the fluorination process is more effective for turbostratic than for AB-stacked bilayer graphene. The fluorination changes the electronic structure similarly for the top and bottom layers in turbostratic bilayers. However, the top layer is more sensitive than the bottom layer in AB-stacked bilayers.