When I was in Split some years ago, I had to travel out to the airport during my stay before flying out at the end - and I wound up taking the city bus out to the airport and the Croatia airlines bus back. I actually had trouble finding the city bus stop at the airport to get back into Split (so I took the Croatia Airlines bus instead)- but you wouldn't have to deal with that if departing to the airport.
Still, I too would take the Croatia Airlines bus if you can. The schedule is timed for Croatia Airlines flights, but anyone can take the bus. It's an express bus and costs a little more than the city bus (which makes stops) but worth it. I took the Croatia Airlines bus the final morning to the airport, too, at a very early hour to get to the airport for a 6am flight and it worked out fine despite having to get up at 3am!!!