John Toshack's side have made a positive start to their qualifying campaign, taking six points from their four games so far.
They currently sit third in Group 4, but remain within touching distance of Russia and Germany heading into Saturday's home date with Finland.
Having fared admirably in away contests in Moscow and Monchengladbach, despite slipping to narrow defeats in both games, Tottenham defender Bale insists places at next year's South African showpiece are still up for grabs.
"We are quietly confident," he told skysports.com.
"We came so close to taking a draw from both Germany and Russia. We are starting to pick up now.
"The young squad is starting to pick up a bit of experience and we are confident that we can pull off a few shock results."
Waiting gameAs alluded to by Bale, Toshack's squad is still relatively inexperienced, with a number of talented youngsters having to adapt quickly to the rigours of international football.
However, the likes of Joe Ledley, Aaron Ramsey, Chris Gunter and Bale have not looked out of place on the world stage and the young Dragons may yet secure Wales' first appearance at a major international tournament in 52 years.
"It is a young squad, but football is football and you never know what can happen," added Bale.
"We are gong to give our best to qualify and we will have to see what happens."
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