With some difficulty! There are no organised public tours - you'll need to butter up a TD or two (and don't get me started on the Cabinet corridor of Government Buildings).
As much as the Bank of Ireland is desirable as a location for parliament (incidentally they don't own it anymore, they flogged it a couple of years ago for something like a piddling €15 million), as has been mentioned there is simply no adequate space for the truly enormous ancillary accommodation required, and makes little sense to move from one compromised historic site to another. Security is the other major consideration, and such an exposed site on all sides would probably render it unsuitable. The latter also has the potential to interfere unduly with the character of the main facade, and you could say goodbye to any attempts to declutter the forecourt and increase public access. Saying all that, the Banking Hall would be an ideal space for the DÃ¡il Chamber - I don't see any problem in that respect. TDs could also have great fun marching around Pearce's abulatory corridors West Wing style, with the top lighting and deep shadows catching on blank sheets of vital State documents.
Now this yoke.
As pretty as the chandeliers are with their sparkily candle bulbs (all long since replaced with nasty lumps of plastic CFLs), this area between the house and the DÃ¡il Chamber surely must win the award for the most hideous ceremonial space in the country. When the Victorians did it badly, my god they pulled all the stops out. And then we added to it with the upper floating bridge decks, reinforced concrete columns with faux marble veining, and head wrecking carpets and curtains. Lovely stuff. The stunning 18th century bookcase the only saving grace.
No I agree Peter that the DÃ¡il Chamber is an elegant space, and very well designed at the lower levels (although recent wheelchair provision has compromised the entire ensemble). No expense was spared back in the 1920s. The problem is the investment stopped half way up, resulting in the upper levels having never been fully resolved. They were added to piecemeal with the public gallery roundabout the 1930s and then the Royal Dublin Hotelesque champange-coloured aluminium glazing arrived probably in the 1960s, infilled in a manner that looks like bare wood and sheets of plywood from a distance. All of this needs major work.
The only reason the entrance hall looks so stunning is because the money was attained directly from Europe in anticipation of one of the European Presidencies. This is one of the few areas where real investment has been made (along with the DÃ¡il bar) including the comprehensive Leinster House 2000 project to the north of the house.
The Seanad Chamber is extremely elegant, but overly cramped, and regardless of aesthethics one would have concerns about the affect of such heavy use on the fabric of the building. What level of structural intervention is required to sustain this use into the future? The PVC secondary glazing is similarly unacceptable but is obviously there for a reason associated with the Chamber...
Personally I think both the house and parliament would benefit from the removal of the Oireachtas away from the main house in favour of a new build on the Lawn. I'm in two minds about the Dail Chamber itself however - it's really of such quality and iconic status to warrant full retention at its present location. The potential for a dramatic contemporary roof structure encasing the historic furnishings however is a concept I find very appealling. This would also serve to highlight the original fittings, a rare example of 1920s furniture design in Ireland, and the last gasp of the classical school and indeed that of large scale mahogany installations on a European level.