With Proton 3.16-6 you will need to download an updated ntdll.dll.so and configure a special launch option in order to save game settings.
1. Download bayonetta_ntdll_override_3.16-6.tar.gz and extract it to /steamapps/common/Bayonetta/
2. Set the following in launch options
LD_PRELOAD="${LD_PRELOAD}:./ntdll_override.so" PROTON_FORCE_LARGE_ADDRESS_AWARE=1 PROTON_NO_D3D11=1 %command%
3. Gun heels!