Yes, I booked things separately for the coastal bus etc. I went in August, so that might affect how often the buses went. I was able to see the timetables of the trains and the buses via apps - I booked the train tickets the day before, and I think I bought a 'rambler' ticket for the bus, possibly attached to the train ticket or otherwise in advance, and I could use it all day on the bus. There was a general northern ireland transport app - not that great user interface but did give me the timetables I needed for the trains and buses. I remember having an app that showed where the bus was (I think it's the Bustimes.org website) so that I didn't miss it and could plan the journey. I took the train from Belfast to Coleraine, and the bus station is right there at the train station, so very easy to change. The bus stops at the different sites, though you might tell the bus driver where you are going to make sure you don't miss it. I stopped at Giant's Causeway first to get there before the crowds, and I didn't book anything there. I then booked a ticket at Carrick-a-Rede once I knew what time I'd be finished at the causeway and which bus I was getting, and that worked fine. I then took the bus to Ballycastle and had a quick look around, but not that much to do when I was there (I was by myself) so just went for a walk, saw the sea, had fish and chips as a very late lunch, and then took the bus back, and stopped at Dun Luce castle as my last stop. Then took the train back to Belfast in the late afternoon/early evening. I didn't stop at any other places but I did look from the bus - it's a pretty journey! The coaches also stop at some of the Game of Thrones sites, but I don't watch it, and though they looked pretty, they weren't enough to make me want to do it that way. They stopped at Carrickfergus castle I think on the way, but only for a quick look from the outside, and I figured that I could always take the bus/train there for a separate visit another day if I really wanted.
It was remarkably easy. I'm not an intrepid traveller and would usually opt for something like a coach tour, but I really wanted to see Giant's causeway when it wasn't crowded, and was really pleased how well it all worked out. I took the train about 7am or maybe earlier, to line up with the first bus of the day from Coleraine. It was much cheaper than the coach journey as well. And I could choose how much time I wanted to spend at the various sties. Also the coaches aren't allowed to go to the Carrick-a-Rede bridge any more - they can go to a viewing place to see it, but can't go into the site. So you'd have to do that on the bus or hire a car. A car would have been fine, but I was on my own and didn't want to hire and drive in a strange place, and concentrate on the road and miss the scenery! It's quite a walk at the rope bridge, so you need to allow a fair bit of time, and I spent a couple of hours or more at Giant's Causeway too, doing the longer walk. So it took me much of the day in the end, but I was really glad I did it on my own rather than the tour.
You can also use an app to buy tickets for the bus from the airport into the city, though I was at the international airport - maybe that's not such an issue at the other airport. But at the international one ,there would have been long queues at the bus itself, but already having a ticket made it faster. Maybe not needed at 7am though!