Hi Janice,
How nice that you are coming over to see us soon!
I had a look and both the bus and the train are equally as fast (around 5 hours), even though you'll have to transit through Dublin in both cases. You'll transit in Dublin City (Heuston Station then Connolly Station) with the train, while you'll just transit in Dublin Airport with the bus. The latter may be more convenient if you want a bus-to-bus option, I would say
Feel free to have a look at
Transport for Ireland's website for more information on tickets and schedules. You can also use the
Rome2Rio website for more info on these itinerary options.
If you need tips to discover
Belfast and its surroundings, please let us know!
Cheers,
Antoine