lancer525,
The blueprints are in the National Archives:
http://www.hnsa.org/doc/nara/searchplans/index.phpSearch for "Virginia." Eighteen drawings for the Virginia BB-13 and other ships of the class are listed. Some are paper drawings and some are on microfilm. You can buy copies of microfilm, either on film or scanned images on DVD.
You don't have to hire a researcher if you are patient and persistent. Archivists aren't naval historians or ship modelers, so it may take a few messages to get the desired information. Archivists will tell you Reel Numbers and how to order them. They cannot tell you what is on the microfilm. I have heard that they are allowed about 30 minutes to answer requests. They have been extremely helpful to me, and I have located and ordered plans for several ships from all the way across the continent, using nothing but email.
Ships blueprints are stored on microfilm. They will be in "Record Group 19." Each set of ship plans has a "Reel Number." This is misleading because there may be many actual physical reels of blueprints in a single "Reel Number." Newer blueprints (WWII and after) have a single Index Reel that lists all drawings in the set. Older sets (ships built before WWII) may not have an Index Reel, with seperate indices on each individual reel of microfilm.
Usually Reel 1 contains hull drawings, general arrangement plans and such. However many useful drawings may be scattered through all of the reels. Most of the drawings will be plumbing, electrical diagrams, vent plans, engineering spaces, etc. After all, it is a complete (mostly) set of plans to build the ship!
If you look around on the National Archives site you will eventually find an "ask us" page. Send an email to this address saying that you are looking for the blueprints for the USS Virginia BB-13 in Record Group 19. Ask for the microfilm Reel Number, the number of actual reels of microfilm, and if there is an Index Reel.
In one to two weeks (there are few archivists and many requests) you will get a response from an archivist giving you the information.
NOTE: The National Archives online microfilm search will not return results for ships plans. It is only for historical documents.
Another source of information is the Historic Naval Ships Association:
http://www.hnsa.org/Another source is the Nautical Research Guild:
http://www.thenrg.org/