Monday's Dublin meeting is part of an assembly External Affairs Committee inquiry and is on the day the UK begins the process of leaving the EU.
The fear is a "soft" post-Brexit border between Northern Ireland and Ireland could result in more stringent controls at Welsh ports for freight operators.
First Minister Carwyn Jones has warned that could mean job losses.
The Irish Minister for Transport, Tourism and Sport, Patrick O'Donovan, and representatives from the Irish Exporters Association were among those meeting AMs during the Dublin visit.
The UK's formal Brexit negotiations with the European Commission started on Monday in Brussels.
Launching a paper on Brexit and devolution last week, Mr Jones said the question of Ireland was "insoluble" at the moment.
He said Wales had an interest in the border between the north and south of Ireland because of Wales' maritime border with the Republic.
Mr Jones warned a "seamless" border between north and south, twinned with customs checks at Welsh ports, could provide an incentive for trade to avoid Welsh ports.
Freight operators could "go through Cairnryan in Scotland, go through Liverpool and go to Northern Ireland then down rather than mess about in Holyhead, Fishguard and Pembroke", he warned.
"So there are job losses there if we're not careful."
The first minister said the Welsh Government was working with the Irish government on the issue.

Former party leader Nick Clegg called her comments "utter cheek".
"It is Theresa May's extreme version of Brexit which will cause real damage to the NHS," he added.
The prime minister gave a speech earlier on Tuesday in which she stressed that she was the best person to lead talks on leaving the EU.
She also told the audience in Wolverhampton: "If we don't make a success of Brexit, we won't have the financial means to fund the public services on which we all rely.
"Our National Health Service - the institution which is there for us at the most difficult times - needs us to make a success of Brexit to ensure we can afford to provide it with the resources it needs for the future."
Mr Clegg responded: "By insisting on dragging the UK out of the single market, she has chosen a UKIP-style version of Brexit which is already causing a squeeze on public services."
"It's time she came clean that the risks are all of her own making. It is her choice to take this country in a dangerous and damaging direction."
The Conservatives have promised increases in NHS spending in real terms reaching Â£8bn extra per year by 2022-23, while Labour has pledged Â£30bn in extra funding over the next parliament.
The Lib Dems have committed to adding 1p in the pound on income tax to raise Â£6bn for NHS and social care services.
They are also arguing for a referendum on the eventual Brexit deal, unlike Labour or the Conservatives.

Mr McIlhagga, 42, was killed by a masked gang outside a house at Riverview Park in Ballymoney, County Antrim, on 3 January.
The Ballymena man was beaten and shot in the leg and died from his injuries.
The three men arrested on Wednesday are aged 24, 41 and 48. A number of other men arrested previously were released without charge.
Brexit's impact on Welsh ports is being discussed as assembly members meet Irish politicians and business leaders.
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The Liberal Democrats have reacted angrily to Theresa May's claim that a badly managed Brexit would mean fewer resources for public services.
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Police investigating the murder of father of five Brian McIlhagga last week have arrested three men.