Ground Transportation from Shannon Airport to Galway

Yes, Bus Eireann route #51, hourly from 0754 to 2054 hourly- journey time 1 hour 50 minutes

https://www.shannonairport.ie/bus/

I am in Galway now having just taken the 51 bus exactly as described. It was 29 euros for two of us. I used cash from ATM in the airport.
They take CC. The bus stops directly in front of the small terminal.