Hi SDevon,
there are a few things other than the cap badge which may help identify the uniform,
The lanyard on his left shoulder suggests some involvement with artillery.
The leather belt with the ammunition pocket (bandolier) was usually only worn by those with warrant or commissioned officer status, it may also indicate a light artillery connection.
The stick (if it is part of the uniform and not just a walking aid) may indicate sergeant major or regimental sergeant major status, it is not the standard 'pace stick' but not all officers or regiments used the standard stick.
The spurs ( as already mentioned) are probably indicative of cavalry or light artillery (if he is in his standard uniform), but officers dress uniform for all regiments had (still has?) small spikes or spurs as a standard part of the footwear, irrespective of whether the unit had any involvement with horses.
so taking all those elements into consideration I would guess that he was an officer in a light artillery regiment, possibly a sergeant major. The suggestion of Iniskilling Dragoons would fit perfectly with this as they were a cavalry / light artillery regiment at the time (a dragoon was a type of musket designed to be used by mounted soldiers).
As for the question of how a Bucks man would have ended up in an Irish regiment.... Units did not enlist solely from their local area, and they did move around a bit, so someone signing up would have been placed with whatever regiment needed people and might have been stationed in the area at the time, some of my ancestors enlisted in Kent and were put into Scottish regiments!
There are a couple of books I can recommend for further research into the pic and the cap badge...
'Identifying your WW1 soldier from badges and photograhs', by Iain Swinnerton,
and 'British army cap badges of the 20th century' by Arthur Ward,
your local library should be able to get copies of both these titles.
Hope this helps
Jon