Hey Todd,
The most straightforward way to accomplish this would be to set your module up in a way that the features you would like to restrict would require Edit rights, whereas the "general" functionality would be available to those that have view rights.
If you added to the module settings with your own custom settings, these are already only available to those who have edit rights. However, if currently you have your "Add/Edit" control (assuming you have one) set up as an "Edit" control in your module registration - you'll want to change this to "view".
You can then give "registered users" permission to view your module. Because the registered user will not have "edit" permissions, they will not get to see any of the other settings.
*edit* wanted to clarify that for this module (and potentially the page) only the "Registered Users" role would have the ability to View -- "All Users" would not, and only Administrators would have the ability to Edit. This should be the appropriate setup - if not let me know and we'll figure it out ;) *edit*
Hope that helps!
Take care,
Ian