We need a bit more information to know what might be wrong here. Are you adding the images via the image section of the Design section, or are you manually putting links in to the images on your computer? To make the images show up correctly they need to be referenced correcly.
Import your images to a location in the Images area of the Design panel, then drag that image to the location of the page you want it in (into the column or whatever type of container you have set up for them).
Once you do that it will automatically reference the correct location for them.
If you are trying to reference images that are not imported, you have to use Absolute URL's for them to work as BSS will not know where those images are, and right now it's not equipped for giving it a local location. We, as users, are hoping to see a feature added in the future that allows us to reference a local directory as the project directory so we can reference files that are not imported, but we don't know if that's coming or not.
The correct way to do this though is to import your images and drag them where you want them.
BSS creates an "assets" directory which contains all files for your site other than HTML pages. This is why it usually doesn't work if you manually add the source link to images.
Let us know if that helps at all and if not, please give us the steps you are taking to add your images to your project.
Just from looking at the first image in your original post, do you have that background image on the BODY element? Or, the div that you have selected in the Overview pane in the first screenshot image you posted?