I think their connection was less deep than most realised. Blair felt he "owed" Clinton, as Clinton showed the way for how left wing politicians could win office.
BUT: the "friendship" did not survive Clinton's jealousy of Blair - during Kosovo, Blair seemed much more purposeful and got better press than Clinton did. Also, Blair was contemptuous of Clinton in private - the running joke among Blair's aides was "Bill gives great blow", meaning he talks a good game but does nothing.
So it was less rosy than first suggested. And it probably still is. Bush simply has none of Clinton's malice or ego - Blair is absolutely delighted and relieved, apparently, to be dealing with a President who means what he says.
Regards, Ivan
Did Clinton "solving" the Ireland problem endear him or isolate him? I would think that one-upping Great Britain (and claiming credit for the resulting "peace") would NOT be good politics (but great legacy). And since BJ was all about me-me-me, since his presidency would eventualy be over, friends were not as important.