When installing as a mod, Civ4 requires the files to be installed in the Assets folder. Delete the empty Assets folder that got created (right-click it and select Properties, it should say there are 0 files in it), and rename CustomAssets to Assets.
Edit: Actually, I don't see how BUG files are being used at all. The CustomAssets folder should be ignored, and that's where all the BUG code is, so how is the game even seeing it? Also, make sure you name your mod folder "BUG Mod 3.5.1" exactly.