In fairness to Mulryan ... he mentions in this book that Bushmills Distillery has no direct link to the 1608 licence to distil. However the Bushmills marketing Department continue to use this ludicrous date as some sort of Badge of honour

. They have even decided to redesign the bottle to incorporate the impressed date of 1608
What is true is Bushmills (The Town) has had long links to distilling and obviously pre-date 1608 but that would of been prevalent all over the celtic kingdom which include current day Scotland and Ireland. There is no direct proof of a continuous distillery working in the Bushmills area from that date through to modern times.
I even have suspicions that the original Establishment date of 1784 that was used pre 60's maybe tentative. But it appears there is evidence that there was a distillery established on the current site in 1784. But numerous distilleries opened and closed i Bushmills during these times.
1761 is the first time that any sort of registration methods were used so we'll probably will never know what was going on prior to that to any certain. However even then is was voluntary so not conclusive. 1766 saw 45 registered distilleries in the Coleraine area which include 4 in the Bushmills area but it is thought that at least twice that many existed in te entire area. How Bushmills can attach it self to any single one is questionable.
I'll give them the benefit of the doubt for 1784 but anything prior to that is pure wishful thinking.
All in all it's a well writen and nice book and has a good history on Bushmills.