Microfilmed Prisoner-of-War records indicate that Bishop was sent to Louisville on December 7, 1863 "For Exchange". That is from "Selected Records of the War Department Relating to Confederate Prisoners of War, 1861-1865" Roll: M598_39

Another record indicates that Henry W. Bishop of the 54th Virginia, "Enlisted in U.S. Navy & sent to Camp Douglas January 25, 1864." Roll: M598_131

It appears that for some reason, Henry was not exchanged. Could have been government red tape, or perhaps he did not wish to be exchanged. The biographical roster in the book 54th Virginia Infantry by Sherwood & Weaver indicates that he was AWOL on May 1, 1862, refused to reenlist and then was conscripted and reassigned. Bishop may have viewed the U.S. Navy as a way of escaping prison life.

Family files indicate that he married in 1866, had 11 children and died in 1926. Occasionally, he is called "Wesley" on census records. One family source states that he was nicknamed "Heywood".
----------------------------------------------
The following is from:
http://www.bitsofblueandgray.com/october_1998_firesides.htm

Service Records of Sailors. For records of sailors who served in the Union Navy, contact the National
Archives. The weekly returns of enlistments, 1855 to 1891, are the records of most value for sailors,
particularly those who served between 1855 and 1865. They have not been filmed and are available only
at the National Archives in Record Group 24, Records of the Bureau of Naval Personnel. Entries list the
sailor's name, enlistment date, birthplace, age, occupation, personal description, data of or return of
enlistment, and record of precious naval service.

An index to sailors who enlisted between 1861 and 1865 is listed below:

Index to Rendezvous Reports, Civil War, 1861-1865. National Archives Microfilm Publication T1099.
(FHL films 1,570,558-88; FHLC computer number 462166.).
-----------------------------------------------
See also:
http://www.rootsweb.ancestry.com/~mscivilw/galvanized.htm