From what I have read - most were re-inerred after the war. The Government only contracted for Federal Soldiers to be reburied in National Cemetaries, the Confederates were more often than not left where they were.

Here is what one source quotes:

By 1883 over 250,000 Union soldier’s re-interred in 79 National Cemeteries.

34 bids were submitted under Government contract from $1.59 to $8.00 per body.

John Walsh