nothing on Google maps, is there. There's a timetable here
http://www.mladifest....rje/obvestila/bus.htm
but it looks as if you have to stay the night. It's not all that far - coach trips regularly do day trips from Dubrovnik to Mostar (further inland) and back. Maybe you could get a taxi?
More information here
http://bhtourism.word...from-dubrovnik-tours/
You just cross the border once each way. I did it en route to Mostar on a tourist bus and the crossings only took 10 minutes or so, but I don't know if that's true of public transport.