It's great to hear that you'll be coming over to visit Ireland in July. I'll be happy to help you out with your public transportation
For travelling from Dublin Airport to Dublin City centre, you have a few different options. These include Aircoach, Dublin Express, and Dublin Bus.
Looking at options for July 7th
, there are two buses to the city centre that you could potentially take. One is with Dublin Express which leaves at 22:55. The other is with Aircoach which leaves at 23:39. Both buses take around 15 minutes to reach the city centre (stopping at Dublin 3arena Point Village & Ringsend).
As for travelling from Dublin City centre to Bray, there is a Dublin Bus
that leaves Leeson Street (Stop 2795) at 23.40. Providing you are able to take the Dublin Express bus from the airport at 22:55, you should be able to take this one. That seems to be the last bus leaving Dublin City travelling to Bray.
There is also a train option. An Irish Rail train
leaves Lansdowne Road railway station at 23:43 and arrives in Bray at 00:19 on July 8th.
Things, therefore, could get a little tight, especially if there are any delays with your flight. One other quick and handy option to get from the airport to either the correct bus stop or train station would be to take a taxi
, of which there are plenty at Dublin Airport.
I hope this information will be helpful to you.