is there bus transportation from Shannon airport to Ennis?

Bus #51 hourly and direct- https://assets-us-01.kc-usercontent.com/db136e73-39a4-0017-c8cc-5f063ce7fc95/23689fca-e9fc-4eb7-8eea-9610fee10ab4/timetable-51-jun25.pdf

There is also an hourly #330 which goes round all the villages, and takes over twice as long - avoid that one.

We took a taxi directly to our hotel. Cost was about €45 with tip.

You'll be jet lagged and uncomfortable. Take a taxi.