Directions from Shannon Airport to Mallow/Longueville House by car are here. 

To go to Mallow/Longueville House by public transport:

1. Take the Bus Eireann service 51 from outside the terminal to Mallow.  The journey time is 1 hour and 50 minutes.  The ticket cost is €13.50 one way, €20.70 round trip.  Tickets can be purchased on the bus or online.
2. From Mallow take a taxi to your accommodation.  Longueville House is about 4 miles from Mallow.