Having lost all seven of their Test matches since winning the Grand Slam last year, the holders approach the game desperate for a win.
Ireland's recent record against the Dragons is poor: they have lost their last three meetings, including the 2011 World Cup quarter-final, but former Ospreys winger Bowe says the scrutiny is all on the hosts.
"They are under a lot of pressure," he said. " Wales haven't been very happy themselves the last couple of games and Ireland will go over there and try and work on that loss of confidence and silence the crowd.
"I would be hopeful Ireland could go over there and get a win. We are still very much hurting from the (World Cup) quarter-final and the first ( Six Nations) game last year – so we know how big this game is.
"To lose the way we lost last year – where we didn't play very well but got ourselves back in front with a few minutes to go and conceded the late try – was heartbreaking. That was the end of the Six Nations for us.
"It is very important to get off to a winning start and build the momentum from there. You could see their tails go up from that."