In 1865, Washington Duke would have most likely traveled from New Bern to his home in Durham by the route of the North Carolina Railroad which passed through Kinston, Goldsboro, Raleigh and Durham on its way to Greensboro.
From the North Carolina Railroad Company (NCRR) site.
In 1848, the N.C. legislature passed a railroad bill calling for an east-west railroad to connect the coastal plains with the Piedmont to open the state for economic and industrial development.
1849: The NCRR chartered a 223-mile corridor between Charlotte and Goldsboro. Goldsboro was also on the Wilmington & Weldon Railroad.
1856: A train ran the entire length between Charlotte and Goldsboro.
1861-1865: The NCRR was an important Confederate supply line. Goods brought in through the blockade at Wilmington could be shipped from Goldsboro westward to Raleigh and the Charlotte Navy Yard.
But increased traffic and reduced maintenance led to a poor road and rolling stock conditions.
April 1865: Several NCRR structures, bridges and miles of track were destroyed during the final weeks of the war.
A map of North Carolina Civil War Railroads shows one going westward from New Bern to kinston and then through to Goldsboro and on to Raleigh and Durham.