You need to find the `bpy.data.images` entry for the image.  If you know the name of the image but not the path you can use `bpy.data.images[NAME]`

Once you know the entry, the full file path is in the `filepath` member, so something like `bpy.data.images['foo.png'].filepath` will return the full path to the image.

If you don't know the name, but you know you have only a single camera background image, you can use `bpy.data.cameras['Camera'].background_images.items()` to fetch a list of all of the background images associated with the camera.  Here's what the list looks like when there is only one image:

```
[(0, bpy.data.cameras['Camera']...CameraBackgroundImage)]
```

You can find the `bpy.data.Images` entry from the second member of the tuple, so

```
items = bpy.data.cameras['Camera'].background_images.items()
camera_image = items[0][1]
filepath = camera_image.image.filepath
```

Will give you the full path to the first camera background image.  For an non-camera background image you need to find the empty associated with the background image.  Here's how to get the filepath for a background that's associated with an empty with the default name

```
filepath = bpy.data.objects['Empty'].data.filepath
```