Bale, who became the world's most expensive player when he joined Real Madrid from Tottenham Hotspur a year ago for some 100 million euros (79.32 million pounds), believes the 2016 European Championship in France will end the wait.
Euro 2016 is the first to have 24 teams (up from 16) compete in the group stages, giving Bale and the ever-improving Wales the perfect opportunity to compete amongst Europe's elite.
"It's even more exciting, we feel we have a great team that's now been together for a while, and we're full of confidence," Bale told the Football Association of Wales website on (www.faw.org.uk) on Saturday.
"The fact that more teams can qualify this time around just adds to that sense of confidence."
Wales kick off their qualifying campaign for 2016 with an away fixture against Andorra on Tuesday. Their Group B also includes Belgium, Bosnia, Cyprus and Israel.
Wales are by no means a one-man team, with a worthy supporting cast including Arsenal's goalscoring midfielder Aaron Ramsey and Joe Allen, an under-rated yet important part of Liverpool's team.
In defence they also have Swansea City's highly-regarded skipper Ashley Williams and Tottenham Hotspur's Ben Davies.
"We're young, but we've been together now for five, six or seven years," Bale said. "We all feel we're at that stage where we really need to start producing," the-25-year-old added.
"Hopefully the time is right and we can kick on and qualify for major tournaments.
"We have to be confident, otherwise there's no point in us being here. We feel we have a good team, that we're playing good football.
"We have the right staff around us and everything is in place now for that [qualification] to happen. The main thing now is that we have to do the job on the pitch."
Wales's only previous tournament appearance was the 1958 World Cup when the great John Charles led them to the quarter-final where they were beaten 1-0 by eventual champions Brazil.
In 1993, a team containing Ian Rush and a young Ryan Giggs lost 2-1 in their final qualifying game against Romania when victory would have seen them qualify for the 1994 World Cup.
Ten years later they lost a two-legged playoff against Russia, despite drawing the first leg away.
Since then they have made little impression.
(Reporting By Tom Hayward; editing by Martyn Herman and Clare Lovell)
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