Is there a border run bus from Prachin Buri to the Thai border or do I need to go through Bangkok?

Yes, there are vans that run to Aranyaprathet from Prachin Buri. They can be picked up outside the big army base and stop at Kabinburi and Sakkeo before reaching Aranyaprathet. However, it is advised to consider other options as the border crossing at Aranyaprathet is known to be difficult. An alternative is to go to Bangkok and then travel to Kanchanaburi for an easier border crossing.