"The expectation is if we do our business correctly and accurately - discipline and defence - there is no reason why we can't win the match against New Zealand and then roll on to the Australia game and use the same process there," said the Connacht supremo.
"I think this Ireland team is a very strong one and an exciting one. You've a lot of experience in the pack and you're going to need that against a side like New Zealand. It has a very good balance to it."
As a player, Bradley was agonisingly close to helping Ireland claim that history-making first win over a Kiwi side. He played at number 9 in the Ireland team that toured in 1992 and lost 24-21 at Carisbrook in Dunedin.
Recalling that tour, he said: "The first match (in Dunedin) was great and we were quite close to winning the match. We were a couple of inches away from an intercept try.
"The second match was here in Wellington in Athletic Park in possibly the worst conditions of all time! New Zealand got their revenge and put a big score on us (59-6).
"Both games were extremely competitive despite the difference in the score-lines and they were enjoyable games to play in."
As an Ireland and the British & Irish Lions player, Brian O'Driscoll has some history with New Zealand. Skippering an Irish side to victory over the All Blacks away from home would be a sweet moment for the 29-year-old, particularly after losing one of his close friends last week.
Speaking after the captain's run session, O'Driscoll said: "We feel if we get our game right we have as good a chance as ever. We genuinely felt we had a good chance last time round (in 2006) as well and capitulated a little after 60 minutes, particularly in the first Test.
"We feel as though we certainly have the firepower and the capabilities, it's just a matter of making sure we put in an 80 or 90-minute performance, whatever it takes."
Ireland were forced to alter their starting line-up mid-week when Luke Fitzgerald pulled out with an ankle injury. His replacement at inside centre is Paddy Wallace and O'Driscoll is backing the Ulsterman to star alongside him - particularly in a distribution sense.
"Myself and Paddy, we have been mixing and matching (in the centre in training). Paddy is a great footballer, he's a great versatility to him. He can play 10, 12, 13 and full-back if needed.
"Being a footballer is being a footballer. Often it can just be a number on your back that you start off with, but you find yourself in various different positions around the phases. So I would think that's the way we'll be playing," he explained.
"The one thing is that Paddy is a great passer, a great guy at putting others into holes and hopefully he'll show some of the form that he did in the Baa Baas game last week."