I know there are buses that go from Split to Dubrovnik, but does this bus stop anywhere near Ston?  

The bus from Split should stop at the begining of Peljesac peninsula (where the road to Ston starts). Since I am not sure if the bus will go all the way to Ston I will try to contact the Bus Terminal.
Unfortunately, I am abroad at the moment, you will receive an answer till the end of this month.

Admin

P.S The "transportation by buss" section will also be updated with timetables and other useful info soon...

Hello

Check at Split's main bus station is there any buses from Split to Island Korcula: If so, that bus will stop in Ston.

kind regards

At the moment there seems to be no direct conection between Split and Ston. There are informations that a Korcula bus company could have such lines available till summer, but we were unable to receive any timetables at this point.

We did find out that the regular bus from Split stops at the begining of Peljesac peninsula. From there you could take a local bus line because the bus stop is 20 meters down the street. The timetable for local lines till Ston and other timetables will be published on Dubrovnik Online transportation section as soon as they are available.