Tickets are sold with allocated seat numbers. The ticket will inform you which platform the bus will arrive at, and luggage is stored in the holdall for a small fee (about one euro). Arrivals and departures are not always announced, so the onus is on the tourist to find the right bus (a sign in the front window of the bus will confirm the right vehicle).
Buses are reasonably modern and the network is fairly efficient, with competition from numerous private companies keeping costs down. For travel from the coast to Zagreb, it is worth checking if the bus company travels on the motorway or the old road. A typical journey from Split to Dubrovnik is four hours and Split to Zagreb around five.
Buses tend to stop for ten minute breaks every couple of hours or so, or for a 20-30 minute meal break on longer journeys.
There are border crossings at both ends, but they are some of the softest in Europe, with the majority of traffic assumed to be transit through to the other part of Croatia. As a general rule, those not needing visas for Croatia will also not require one for Bosnia, and those who do will. Panicky posts on various travel forums are a regular occurrence every Summer, as tourists with visas for Croatia discover that there is a border to be crossed.
To be absolutely sure the advice would be to take the ferry, but in practice, there should be no problem on a bus bound for Split or Dubrovnik. A definitive official statement is hard to find, but the closest official advice is on a forum thread about crossing the border at Neum, including this emailed answer from the Croatian Ministry of Foreign Affairs:
Please be informed that according to the Agreement on a free transit through the territory of the Republic of Croatia to and from the Port of Ploce and through the territory of Bosnia and Herzegovina at Neum from the 22 November 1998 on the International border crossing Klek-Neum and Zaton Doli - Neum there is no border control for the foreigners who are transiting without stopping (by using the green track) through the Neum corridor.
While Starigrad is served by bus collection, the catamaran to Jelsa is not, and more than one tourist has spent more time than planned in the eastern port town on Sucuraj, due to the lack of public transport (traffic is sparse even in peak season once the cars have disembarked from the ferry). It should also be noted that the high season ferry to Starigrad from Split at 0130 is not met by buses or taxis.
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