If you are on holiday in Croatia, and wish to visit or continue your travel to the neighbouring country Montenegro you can do so with direct public bus. Whole year around there are buses from Dubrovnik to towns like, Budva, Kotor and Bar in Montenegro, in the summer season, there are additional departures from Dubrovnik as well as daily buses from Zadar*, Zagreb* and Split*. The travel time from Dubrovnik to e.g. Kotor 2.5 hours, from Split about 7 hours, from Zadar about 9 hours and from Zagreb a bit more than 12 hours, depending on which departure you travel on. You have option to exit the bus in the following cities in Montenegro, Herceg Novi, Tivat, Kotor, Budva, Bar and Ulcinj. Obviously you also have daily buses travelling in the opposite direction. Here you can see time table for some of the most popular travel options

Zagreb to	Zadar to	Split to	Makarska to	Dubrovnik to
↓	↓	↓	↓	↓
Igalo	Igalo	Igalo	Igalo	Igalo
Herceg Novi	Herceg Novi	Herceg Novi	Herceg Novi	Herceg Novi
Kotor	Kotor	Kotor	Kotor	Kotor
Tivat	Tivat	Tivat	Tivat	Tivat
Budva	Budva	Budva	Budva	Budva
Bar	Bar	Bar	Bar	Bar
Ulcinj	Ulcinj	Ulcinj	Ulcinj	Ulcinj

Alternative to the direct buses mentioned, you can basically arrange travel from any other city in Croatia, doing so you will have to take bus from your starting point to Split or even better to Dubrovnik, and then change to one of the buses driving to Montenegro. Please note that the Dubrovnik buses all departure from the main bus station and not from the airport. If the buses from Dubrovnik should not match your travel schedule, you alternatively have option to arrange for a private transfer, you can see prices for private transfers from Dubrovnik here *These departures might require bus change.