Greetings!
It is not possible to use Bing Maps Aerial imagery online service with Image Classification tools.
However you can export your Bing Maps imagery, once you have added Bing Maps imagery into ArcMap and then use it for Image Classification purposes.
You can export the map as a GeoTIFF - File > Export Map (save as type: TIFF) - General option: change resolution as required, & check on write world file. - Optionally, from Format tab, you can check on write GeoTIFF tags.
Hope this helps.
Thank you.
