The best way to get around the state is by car.
By Official Transit
Information on North Dakota Transit can be found here (http://www.apta.com/links...)
By Rural Bus
Jefferson Bus Line 888-864-2832 has a route that goes along US I-29, which goes north and south.
Greyhound 800-231-2222 goes along the other major interstage, I-94, which goes east and west.
New Town Bus Line 701-852-2477 starts in New Town, ND, heads east on Highway 23 up to Minot, then continues on Highway 2 to Grand Forks. It always runs from Minot to Bismarck on Highway 83.