Direct transportation Shannon to Dublin

I suppose that depends on your definition of "direct" - and your tolerance for jumping though hoops which may be expensive, time-consuming, inconvenient, or (probably) some combination of all three.

You could take a bus, but it appears there would be a change or two. This would probably be the cheapest options, but probably not a lot of fun (especially after a long flight). You could take a bus (or a taxi) to a train, but with less-frequent service that might cut things close for you. Possibly inconvenient schedules.

I see in your other thread that you are trying to get to Dublin for things that need to happen the following day (?) so adding time-pressure to your already-challenging circumstances.

Rome2Rio lists some options, none of which are particularly appealing to me, but might work for you in a pinch - look here. Rome2Rio isn't perfect, but I find it is often helpful in giving me a reality check. There may be other options not listed there, but there might not be. If it were me, I'd find some way (bus, taxi, whatever) to get to a train station and take the train the rest of the way, but check the schedules carefully (you don't mention what time your flight arrives and how much time you really have to get to Dublin). The trains are reliable and comfortable, run on regular schedules, but in your situation may be cutting it close.

As you have probably already concluded, Shannon isn't an ideal landing point for what you are trying to do. And while Ireland is lovely, getting around some parts of Ireland may not always be as quick, easy and efficient as one might expect. It's still worth going.

Good luck with your plans.

David, I will take your advice. Taxi to the train. Thanks

Rome2Rio talks a load of utter bunkum far too often. No one in their right minds unless they want to see much of the country is ever going to go bus Shannon to Limerick, then bus Limerick to Waterford, then bus Waterford to Dublin.
The express bus #51 runs every hour at 50 past each hour from Shannon Airport to Limerick Bus Station- co existent with Limerick Colbert railway station, then train as in your other thread.
The #343 runs every 20 minutes but takes an hour as it also serves a lot of local traffic. It is generally run with double deck coach-buses where your luggage goes in the hold.
The trains are meant and timetabled to connect at Limerick Junction where it is a cross platform interchange.

I’ll vouch for David, we took a cab to Limerick train station after landing from Shannon at 6am and took the train to Dublin in March. Very comfortable train ride and affordable as well, especially nice not having to drive after the overnight flight. However I will mention that the ride was very noisy bc it was the day before St. Pattys day and all the college students were starting to party lol.