Dubrovnik public transport is very well organized and operates a network of over 10 reliable bus routes. Buses usually start running at 5 a.m. and stops around midnight, even though there are night lines as well. Libertas Dubrovnik is the official company that operates the routes connecting all urban and suburban areas of Dubrovnik. Bus tickets can be purchased directly from the driver or at kiosks of Libertas or TISAK that can be found almost at every bus station. If you buy a ticket directly from the driver, the price is 15 Croatian Kuna, but if you buy it at the kiosk the price is 12 Croatian Kuna and it is possible to pay only in cash. The ticket is valid 59 minutes from the validation / stamping and can be used in all directions. There is also a daily ticket (30 Croatian Kuna) which lasts 24 hours from the first stamping and there is no restriction in the number of trips. Children under 6 years accompanied by an adult do not have to pay for the public transport. If you don't have a ticket or is not properly stamped, you will immediately have to pay a fine the amount of 100 kn to a bus conductor.
Buses cannot enter the Old Town and they leave you at the bus turnaround point called Pile Gate, located just next to the entrance to the Old Town. Towards Lapand and Babin Kuk, buses number 4 (Lapad) and 6 (Babin Kuk) run every 10 to 15 minutes. Towards the ferry port and the main bus station Gruž you can take buses number 1, 1A, 1B (Mokošica), 3 (Nuncijata) and 8 (Viktorija).
You can see a map of all city buses here, and here you can see departure times of the city buses.
In addition, city is very well connected with suburban places, the most popular being a connection to Cavtat along with Slano, Molunat, Plat, Srebreno.
Bus number 10 runs to Cavtat every 45 to 60 minutes and the starting point is from Gruž in Dubrovnik. Driving towards Cavtat lasts 25 minutes and the ticket price is 25 kn.
You can see here timetable for suburban bus routes.
The company Libertas also has a free phone number 0800 1910 to which you can refer all inquiries or complaints relating to public transport.