I understand your nervousness, but that's a part of why this community exists! It's a way to plan and experience so that when you do pop by you can have the very best experience possible.
There are a number of resources available to make planning your visit as stress-free as possible. The first is the RomeToRio
website, which is incredibly helpful in finding transportation between any two locations. I already filtered for your destination and it looks like there are a few options available. Based on your schedule, it seems like taking a rail to Sligo and then a bus to Ballybofey might be a reasonable option. The train leaves at 19:05, which is a bit later than you were planning. Still, that means that if your plane is running late, then there's no risk of missing your train. In addition, rails are an amazing travel option and I'd highly suggest this article about public transportation
If you do choose this option, I'd love to recommend some quiet spots in Dublin to relax in while waiting. There's nothing better than a good, hot meal after a long plane ride, and there are some wonderful places in Dublin I hope you would love.
Another option I found is through Translink, which would be to take a bus to a more populous city like Strabane, and then continue on to Ballybofey once you arrive. This does have an option closer to 17:00, with the earliest bus leaving an hour later at 18:00. However, looking at these timetables, it does seem like you would reach Strabane at 21:10
and there wouldn't be another bus to Ballybofey until 8:35
the next morning. If staying overnight doesn't appeal to you, then I would suggest the rail option above.
I do sincerely hope that these options fit your schedule! If you'd like more information, please don't hesitate to reach out. We're all here to help!