Well said BillieBob
birdlady, if you register directly with Bristol you will be signing up to study for your ATPLs with a CAA approved school. If you want to train for the CPL in Ireland you will have to go through all this hastle of getting the IAA and CAA to accept a transfer of state of license issue.
BUT, if you sign up to Bristol through Pan Aviation, panaviation.ie, you will be signing up with an IAA approved school and will be studying the Bristol course but sitting the IAA ATPL exams in Dublin. It's exactly the same course, the only difference is that your two week brush up course is in Dublin and your exams are in Dublin. It's also more expensive but what isn't in this place.