Basically, I'm wanting to make it so specific groups will be limited to a set bandwith per week or month or something.
Nothing even remotely like that available out of the box. You could add a field to the user table that would store the file size of each image that is clicked for a particular user, then add the code to add the filesize when each image is clicked, and add code to check to see how much is available before displaying the image to verify the user hasn't exceeded the limitation. There would also have to be a field that stores a date of the first use of the bandwidth, and code would be needed to check the date against the current date and reset the bandwidth if the date is greater than a week. You'd also have to add code that would allow you, as the admin, to set bandwidth limits either for a group or for each individual.
It's possible. Perhaps you could post a request on the freelancers board requesting this.