Getting around in Bhubaneswar does not take much time. Town buses ply throughout the city. These are government-run and cheap. Fares are very reasonable. Tickets are bought on the bus. You can pay cash. Apart from this, the state has already launched the DTS city bus service which operates around the city with 15 mins difference.
Auto-rickshaws can be found on most streets of the city. For the budget traveler, Bhubaneswar offers shared autos, where you can make journeys even for INR 5/km.
There are several taxi companies operating in Bhubaneswar as well as app-based taxi services like OLA and UBER. They charge by the distance. There is a minimum fare for first few kilometres and for every subsequent kilometre they charge in increments.