Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Bangkok to Split as you normally would.
Split (SPU) is the airport you will fly into if you book a flight from Bangkok to Split. You should not have trouble finding flights to Split from Bangkok; the airport handles an average of 0 inbound flights from Bangkok per day. You should also have plenty of airline options to choose from since 0 airlines have flights to the Split airport from Bangkok. It is only a 11.9 km journey from Split (SPU) to Split’s city centre.