Bismarck Municipal Airport (BIS) has direct flights to Minneapolis, Denver, Chicago, Dallas, and Salt Lake City, among other hubs. Car rental is available at the airport and is strongly recommended — Bismarck is a car-dependent city and most of the interesting sites around it require driving.
By road, Bismarck sits at the junction of Interstate 94 (east-west, connecting Minneapolis to Billings) and US-83 (north-south). From Minneapolis it is about 6.5 hours; from Billings, Montana, about 3.5 hours. Amtrak's Empire Builder runs through Mandan, just across the river, once daily in each direction (Chicago–Seattle), but Bismarck itself has no train service.