Getting from Leeson Close (Hotel Number 31) to Dublin airport

Have you checked Rick's Ireland tour book? I believe it mentions two different buses. They take different routes so the best one will depend on where your hotel lies in relation to the routes.

I used the Aircoach.

I felt is was very reasonable. I believe it was betweem 7 and 8.5 euros each way. They do have the options to purchase a round trip fare.
www.aircoach.ie
I also understand that you can make a reservation online too. I didn't.

I used the air coach as well just two days ago. Very simple and well marked. 8.50 Euro for a one way ticket. Bus driver is friendly, but fast, so know where you are going and they will tell you the stop.

As others have said, AirCoach is one option, which I highly recommend. You can also take the AirLink bus, too. The major differences are that an AirLink bus is a double-decker bus that is more crowded, makes more stops, and you have to take your luggage onto the bus. The AirCoach is a coach bus, much more comfortable and roomy than an AirLink bus is. Makes far fewer stops than AirLink buses do, so you have to look at the AirCoach maps to see if there's a stop near where you'll want to catch the bus. The drivers get off the bus and open the luggage hatch at the bottom of the bus so that you can load and unload your luggage, rather than having to take your luggage onto the bus like you have to do with AirLink.

As for cost, AirCoach is maybe one or two Euros more than AirLink...definitely worth the (small) extra cost!!

Just looked at the AirCoach info...looks like you can take the 700 bus from near your hotel. That bus stops at Leeson Street Lower somewhat near your hotel. €8 Euro per person one-way to the airport. You can book tickets online at the AirCoach site if you wish. Or, I am pretty sure, you can pay the driver when you catch the bus.

http://www.aircoach.ie/timetables/route-700-dublin-airport-dublin-city-centre

Here's the link to download the pamphlet about that route:

http://www.aircoach.ie/sites/default/files/dac/Dublin%20Map%20leaflet.pdf