Hi Babette,
Thanks for reaching out.
You can use a combination of rail and bus, as it might make more practical sense. I would recommend using
Rome2Rio and
Transport for Ireland Journey Planner as resource tools for planning your journey. You can enter your location and destination for each stage of your trip and it will provide you with the different options for travel, as well as times and pricing. In the case of Galway to Derry, there is a bus option - get the 64 bus from Galway Bus Station (stop 555041) to Ulsterbus Depot. The bus runs five times a day, you can find out more
here.
Let me know if you have any other questions and I would be glad to help.
Cathaoir