I am so glad you are getting excited about your trip to Ireland. You are most welcome! Melin has told you about the Goldline Express bus to Belfast– the 261a. However, I wonder if you have considered travelling by train.
It would mean first going to Derry/Londonderry – famous as a walled city. From there, trains run every hour to Belfast. The stretch of line between Derry and Coleraine is particularly beautiful - hugging the coast, going through a tunnel under the iconic Mussenden Temple perched on the edge of the cliff, and then along the estuary of the River Bann to Coleraine. From there the train goes inland to Belfast.
However, if you had time on your trip. It would be very easy in Coleraine to transfer to a 402 bus, which goes along the stunningly beautiful Causeway Coast (named after the famous Giant’s Causeway – worth seeing) to Ballycastle. https://www.translink.co.uk/timetables
From there you could get a 131/217 bus to Ballymena, where you could pick up a train again to Belfast.
You needn’t worry about transferring between buses and trains because stops and stations are in the same place, and anyway, local people are always very happy to help. I suppose it depends on how much luggage you intend to bring and on how much time you have available to spend in getting to Belfast. So now you have another option to consider. :)
I hope your plans come together easily and that you have a great trip.