The largest and the main Bus stand for Bhubaneswar is located at Baramunda, and in common language called Baramunda Bus stand. It is located nearly 10kms away from the Railway Station. Another small bus stand is at Master Canteen (Bhubaneswar Railway station Pf 1 side).
If you are alighting at Bhubaneswar station, and wish to go to Puri, then go to the Bus stand towards Pf 1 on the railway station, and you can get Govt AC Low floor "Mo Bus", but they are non-frequent. Instead, you can come outside from Platform 6 side, and walk to the Cuttack-Puri Road which is roughly 200m away from the station, From there every 15 min at day time and every 20min in the evening...
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time you can get buses to Nimapara, Kakatpur, Puri and Konark. But the last bus passes at about 9:45 pm-10 pm.
If you wish to go towards North Odisha (Jajpur-Bhadrak-Balasore-Baripada), Western and Central Odisha (Sambalpur-Rourkela-Keonjhar-Barbil-Jharsuguda-Balangir-Dhenkanal-Anugul-Talcher), then reach the Vani Vihar square which is nearly 4kms away from the railway station. You can easily get shared autos from the station. From Vanivihar square, regular Balasore/Baripada AC buses can be caught every 20min gap starting morning 5 am till night at 10:30 pm. The same case is also for Western and Central Odisha but the last buses to all routes are at about 10:30-11 pm only. After that, you won't get any buses. Also do keep in mind that, from 6 pm to 8:30 pm in the evening, No buses run for Balasore/Baripada. But always keep an open eye that many times I have seen due to Festive seasons or any other occasions, Police blocks the Vani Vihar square, thus the buses instead of coming below to the square, go via the above Flyover and halts on the highway where the service roads meet the Highway which is roughly a 200m walk from the Vani Vihar junction.
If you wish to go to Southern Odisha (Berhampur-Visakhapatnam-Ganjam-Koraput), then you will have to reach the Baramunda bus stand to catch your bus. Ample amount of Govt and Private buses run between state capital Bhubaneswar and Silk city Berhampur.