The QPR boss insists the Welshman needs to work with the Portuguese superstar while not being intimidated by him if he is to justify his world-record price tag
Bale, who first broke into the Tottenham team under the current QPR boss, eclipsed Ronaldo's transfer record by making an €100 million move to Real Madrid this summer.
And Redknapp believes Santiago Bernabeu's biggest superstar presents the biggest obstacle to the Welshman making a success of his time in Spain.
"His biggest test will be to step out of the shadow of Cristiano Ronaldo with confidence. That won’t be easy," the QPR boss wrote in his new autobiography, serialised in the Daily Mail.
"Ronaldo is a huge star at Madrid and will probably want to take nine out of 10 free-kicks - at least. Gareth will have to assert himself and that will require a strong mind.
"He has to think ‘I’m an £86million player’ and act like it, taking responsibility, claiming the ball when he fancies his chances.
"And yet at the same time he cannot dwell on his fee and what it means too much because that would put him under immense pressure. It is a tricky balancing act.
"He will have to be ready for the matches when he goes it alone, has a shot, misses and Ronaldo starts throwing his arms up in the air.
"He cannot, at that point, go into his shell and become this timid little creature. But it is not natural for Gareth to behave in an assertive way. Don’t get me wrong, he knows he is good.
"The fee is crazy, amazing money, but he wouldn’t have fought so hard to get the deal done if he didn’t fancy his chances of living up to expectations in Madrid.
"Yet, equally, Gareth is a quiet lad, who spends time with his girlfriend and family, and I’m not sure being in the same bracket as Ronaldo and Lionel Messi will suit him.
"If Ronaldo feels threatened by Gareth’s arrival, Madrid could be a lonely place so he will need to lean a lot on Ancelotti, who speaks good English, and Paul Clement, Carlo’s assistant, who is English.
"Luka Modric is another old friend who could help him settle in.
"The one thing the club cannot provide for Gareth and Cristiano is a ball each — so they will need to work hard on that partnership because they are such similar players."
Redknapp insists he recognised Bale's potential very early on - even if the Welshman did seem a little too preoccupied with his hairstyle.
"He drove me mad in training," the QPR boss added. "Technically, he was outstanding but he always seemed to be playing with his hair. It was never right.
"He’d be flicking the fringe or wiping it out of his eyes and I would be going quietly mad, just watching. ‘Gareth, leave your barnet alone! Gareth! Stop touching your hair!’"