Hello Christine,
Yes, it's lovely to hear that you will be visiting Derry and the Giant's Causeway.
As mentioned above by Cathaoir, reaching the Giant's Causeway using public transport requires a combination of bus and train services. The train from Derry once described as "one of the most beautiful rail journeys in the world" is probably a good option to get to Coleraine Bus/Train Station. From the station you can then pick up the 402 Bus Service to the Giant's Causeway.
For the full Giant's Causeway experience, it's recommended to visit the Visitor Centre there. If doing so, you must prebook your ticket online via the National Trust website. Or there is the option to purchase a 'Green Ticket' from Bushmills Visitor Information Centre which covers a return bus journey from Bushmills to the Giant's Causeway and entrance to the Visitor Centre for a reduced rate.
I wish you an enjoyable trip!
Alison