You've accepted an answer, but I thought I'd try to answer the literal interpretation of your question.
As T.E.D. stated, the railroad reached Wheeling, (later West) Virginia in 1853. However, there was no bridge across the Ohio River until after the Civil War. Competition with other railroads prevented the bridge from being built during the run-up to the war.
Following Sempaiscuba's comment, we find a timeline that tells us the railroad built such a bridge between Benwood, W.V., and Bellaire, Ohio from 1866 to 1871. They had to lease track on an existing Ohio railroad (and change the gauge).
(Source: Wikimedia Commons)
(Please note: As the Ford Motor Company was not manufacturing the Grand Torino in 1871, this photo is clearly from much later.)
This bridge still stands with its original stone piers across the river and stone viaduct on the Ohio side.
Also in 1871, the B&O opened another bridge from Parkersburg, West Virginia, and Belpre, Ohio.
So by 1871 the B&O was able to connect Baltimore with Sandusky, Ohio and eventually Chicago.