I will be arriving at Dublin Airport from the US next Monday and would like to shower before heading into the office for the day. Are there any shower facilities available at the airport? I've tried looking at the airport maps, but don't see anything there. Any other suggestions if that doesn't work out? Thanks!
Don't think so, it's still such a small airport. You could head to the swimming pool if it's a public hour.
You kinda need to specify who you're flying with and in which class; if it's biz with Aer Fungus, see http://www.aerlingus.com/goldcircle/lounges/

"Just stand outside the terminal in your shorts.... It's sure to be raining :-)"
No loitering allowed... (rofl)

Never seen or heard of public / customer showers in Dublin airport? However Terminal 2 is brand new so it's possible? Contact the airport authorities:
http://www.dublinairport.com/tns/contact-us/contact-details.aspx
If not there are a number of hotels beside the airport. I'm sure you could work something out?
http://www.bewleyshotels.com/dublin_airport/?r=3759286&gclid=CLjKxJnUsasCFUKEDgodhj3ecA
http://www.radissonblu.ie/hotel-dublinairport
http://www.carltondublinairport.com/?gclid=CKrsgL7UsasCFcWFDgodTUQldA