Can you set up sub folders in the media bin to categorize your content?

Premiere doesn't have a "media bin" so I'm not 100% sure what you're referring to.

If you mean the Project Panel where you have all the media files and stuff for a particular project, like Ann's link shows, yes you can create sub-folders (the folders are called "bins"). You just right click within the project panel and hit "New Bin", and to create a sub-bin you can drag one bin into another, or right click onto a bin and click "New Bin" with it selected.

If you mean the "Media Browser", that just reflects your actual storage drive so you'd create the folder on the drive itself.

In the Libraries panel you can create "groups" and sub-groups.