From Split to Tivat there is a travel distance of about 300 km, trough out the year there is bus connection between the cities, but travel time is about 7 hours. As the bus passes both the border between Bosnia and Croatia and the Border between Croatia and Montenegro, delays can occur during the summer season.
Alternative to the direct route, you can also choose to travel from Split to Dubrovnik where you have very frequent buses, and then from Dubrovnik to Tivat from there on.
You can see timetable for buses between Split and Tivat here: