there are busses from budva or kotor direct to dubrovnik.
This summer there was 3 every day.
We paid 17€ for one ticket from budva.
I can't tell you the exat times, because the timetable is very often changing.
Buy a ticket 2 days in advance and it's ok.
From Durbrovnik to Split there are busses every hourhttp://www.libertasdubrovnik.com/voznired.pdf
This is the Timtable this year.
I can't tell you the price, but i can say that a bus to Ploce costs 9€ this year.
If you have more questions to the busses just ask again