You can find a list of private researchers on NARA's website.

http://www.archives.gov/research/hire-help/

Here is a great book to help identify the records you are seeking:

Preliminary Inventory of the War Department Collection of Confederate Records: RECORD GROUP 109 - Elizabeth Bethel. Indexed by Craig R. Scott.

Like any good Government agency, I'm sure NARA has done some revisions to the scheme.

Finally, here is the NARA site for viewing Confederate Records that are being digitized.

http://www.archives.gov/research/search/

Warning: it can be a cumbersome search process.