To export textures to CityGML you need Bentley Descartes which is included with Bentley Map Enterprise or can be run as a layered application with Bentley Map.
Problem > Cannot export 3D building model with texture in CityGML format thru FME extension.
It’s expected that it doesn’t work if the texture comes from Bentley Descartes. Only Map Textures are supported in the import \ export to CityGML. Bentley Map doesn't have the code to rectify the images to create textures, but Bentley Descartes does have it. However, Bentley Descartes cannot create Bentley Map textures.
So, here is in the document attached the suggested workflow that fill the gap.
6366.test.pdf