Bradley is a big fan of Rooney and the positive impact he has on the England side.
The other side of his game has been in the spotlight this week with Rooney's temperament again called into question after his yellow card against the Platinum Stars.
But Bradley will not try to capitalise on that side of Rooney's nature in Rustenburg.
He said: "I get asked the question about Wayne Rooney all the time.
"I have tremendous respect for Rooney and what he brings to England in so many ways.
"His effort, his competitiveness, his movement, his influence on that team is great.
"But we won't try and wind him up, no. We don't enter into all of that sort of thing."
Bradley believes the USA have developed significantly as a team since losing 2-0 to England at Wembley in May 2008.
He said: "Those kind of games provide good experiences although I don't believe we were overawed that night.
"We have grown as a team a lot since then. We have played a lot of top opponents and those kind of games continue to help us improve.
"There is a core of players that have been through all those experiences, including the Confederations Cup last summer and, from that point of view, I think our leadership is strong.
"Our ability to use those experiences, good ones, bad ones, knowing how to stick together, can stand us in good stead.
"We understand that when we all play as a team, when everyone is committed the right way, we can compete with the top teams."
Bradley believes Landon Donovan and Clint Dempsey can play an important role for his side.
He said: "Landon and Clint are both important attacking players for us and we are very lucky they have the ability to play different roles.
"We have seen that with Clint at Fulham and with Landon at the LA Galaxy and with Everton on loan.
"That is something that allows us to have some tactical flexibility and something we hope we can use at some stage to our advantage."
Donovan, meanwhile, has warned England his side have the ability to produce something "special" on Saturday.
Donovan believes the USA will take great confidence from their performance in last summer's Confederations Cup - also played in South Africa - when they finished runners-up.
They eliminated Euro 2008 winners Spain before losing 3-2 to Brazil in the final after leading 2-0.
But Donovan is also aware there will still be plenty to play for in terms of qualification regardless of whether the USA win or lose against England.
He said: "2009 was helpful in that it gives us the belief that we can do something here.
"Aside from that, that is the past, and so our job now is to focus on the present.
"But we know we have the ability to be special and now the focus is on bringing that out of us every time we play.
"However, we also have to be aware of the the bigger picture in that this is just one of three games which are all equally important.
"We can win Saturday and not advance to the next round still and we can lose this game and still go through."
Donovan added: "Last year (in the Confederations Cup) we thought we were out after two games.
"Then we played well against Egypt and it changed everything. We have to keep the big picture in mind.
"I understand what this game means but there is more to it and we have to be ready to react no matter what happens on Saturday."
Donovan was inspired by the 1994 World Cup in his native country and wants to play a full part in ensuring the United States host it again in the near future.
He said: "I think of how soccer has developed and I know first hand how much we love this sport in our country and how much we have all put into it.
"I think we would all be excited at the opportunity of hosting another World Cup.
"My only regret would not to play in a World Cup in my own country.
"There is no greater place to hold a World Cup and a lot of my efforts recently and going forward will be to try and ensure we get another World Cup."