The Irish have never progressed beyond the last eight of the competition and on two occasions - in 1999 and 2007 - failed to progress that far.
But they have taken 2011 by storm, winning their pool with magnificent victories over Australia and Italy to set up a potentially thrilling contest with Wales.
Followed across New Zealand by a 25,000-strong army of travelling fans and with a great team spirit, the stage is set for Ireland to break new ground.
"We've been very happy with the way the last four games have gone," said Bowe.
"We know how well Wales are playing, they're definitely one of the form teams at the World Cup.
"It's going to be difficult but this is a chance to create history for Ireland.
"There's a huge amount of self-belief in the team. We have a great blend of youth and experience.
"A lot of the players have been in cup competitions and this is an exciting time for Irish rugby.
"This team is in as strong a position as we've ever had. We've got some world-class players.
"In the past we've always been strong going into the World Cup but failed playing against some of the top teams. This time we've beaten Australia and Italy."
The RBS 6 Nations rivals collide at Wellington Regional Stadium on Saturday, but Bowe has revealed anxiety levels are already rising.
"The players' nerves are obviously heightened at this stage of the competition," said the Lions winger.
"It's obviously still early in the week but we know what's at stake. This is certainly the biggest match I've ever played in.
"Wales are always a great enemy for Ireland and we've had some great games before."
Three years at Welsh region the Ospreys means Bowe is on good terms with many of his quarter-final adversaries.
"I always enjoy coming up against the Welsh fellas who I know very well. It adds an extra bit of spice for me," he said.
"But we're well used to coming up against Welsh opposition.
"For the guys who have toured with the Lions there's great camaraderie between the nations. It will be a great little battle.
"I went to the cinema last night and bumped into a few of the Ospreys players.
"That was the first time I've caught up with them and it was nice to have a chat.
"They're friends at the end of the day, so it was just friendly banter, but when we get out on the pitch it will be a different story."
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