Split International Airport is located 50 kilometers north-west from Omis with organized bus transfer of passengers from the Airport to the city of Split. To reach Omis from Split you can use any of the local bus lines going south.
There are regular international coach services connecting Split with all neighboring countries, as well as Switzerland, France, Germany and Slovakia. Bus service between major cities (intercity lines) is quite frequent, as well as regional services.So you easy find connection to Omiš from the Split central bus station.
If you'd like to make a trip to Split (or other places between Omis and Split, like Podstrana, Stobrec, Duce, Dugi Rat...) you can take bus no. 60 which drives to Split.
The price of the ticket, one way is abt. 20-25 kn. You can buy in in the bus.
There are buses going every half and hour, starting from 3:45, until 23:30.
I have put a link of bus company so you can easily check timetable.
Since the web page doesn't have an english translation (at least at the time this tip was written, I'll write down how to surf and get the info you need).
The main search window is the small one in upper left section.
Raspored vožnje autobusnih linija - Bus schedule
Gradski i prigradski prijevoz - city transportation (meaning city of Split and it's bus lines)
Šire prigradsko područje - transportation of suburb areas (these are places not part of Split but are considered it's suburbs, like Trogir, Omis, Solin...)
when you select the line, another window pops up where it shows hours and days. buses usually drive differently for working days and weekends.
radni dan - working day
subota - saturday
nedjelja - sunday
Omis is located only 25 kilometers southeast of Split.Just follow the Adriatic road (Magistrala) form Split to the south.