Bodø is a long, slender city around 2-3 km in width and over 10 km long in a roughly east-west line. This makes communication by bus well established for a city this size, and during weekdays busses go every fifteen minutes to-and-from town westwards. The Sentrumsrunden bus brings you anywhere you want within the city centre, and there are also buses going northwards to the suburbs. The bus system is zonal, meaning that you pay more the further you are going.
There is also a service of regional buses to other cities, but they only depart a couple of times a day, or even more rarely if the distances are long. A bus to Sweden goes on weekends, making it possible to take a weekend trip, Friday to Sunday, to anywhere between Bodø and Skellefteå.
Many international car rental businesses are established in Bodø. The city has a good road network and many scenic roads. A car is desirable if you are planing to stay in town for a while, or see the areas outside the suburban bus network.
Taxis are also available, but with typical Norwegian prices, you should be cautious about using them on longer trips. A 10 km trip costs about 200-250 NOK in a normal size car, and you pay for the trip, whatever the number of passengers. A full car, four people, will often be cheaper than bus fare, to a certain point.
You can also bike virtually everywhere in Bodø and suburbs, and there is many scenic routes to see.