Shannon airport lies to the north west of the city of Limerick and is approximately 120 km (75 miles) from Millstreet. However, there is no easy transport connections to Millstreet, and you should expect that the journey will take 5 hours by bus! Plan your journey using the Bus Éireann journey planner.
Also consider getting the bus to Mallow and then catching the train from there. There is a direct bus from Shannon airport towards Cork (bus number 51) that stops in Mallow. Once there, do some grocery shopping and then make the onward connection by train to Millstreet. You may opt to get to Limerick city and then make your way by train from there, but this will increase the number of connections that you will need to make!