I'm afraid that's the way bundling works.
If this is unsuitable, then the only way of preserving your folder structures, when copying to other machines is to have a rigorous disciplined approach to how you build your workspace. The most important thing is never to target a file that isn't in the same folder as your workspace. A lot of users have adopted this method and never bundle shows.
If you do this then you can just copy the show folder to the new computer, check it by removing the drive you transferred it from and turning the network off and checking that all the target files are referenced from the folder on the new computer.
This also has the advantage that you can include other files that you might want an operator to swap out in the workspace, which would be lost in a bundle operation.
It might be the case that your master show folders are organised this way anyway as the way you describe how your folders are organised suggests you are targeting only from the show folder.
Bundling is only really useful for folks that like to target files from all over their storage. A few sound effects from a Sound FX Library removable, some music tracks from their downloads folder, files copied from the directors USB stick to their desktop etc. etc. Users who work this way are rarely concerned with folder structure in the bundled workspace, and attempting to preserve some sort of folder hierarchy from their working method would probably be highly counterproductive.
Mic