The Welshman, who moved to Real Madrid for a world record-breaking £86m in August, was converted from a defender to a winger under Redknapp at Spurs.
The current Queens Park Rangers boss admitted that he was always aware of the ability of the Madrid man, but said that he needed to harden his approach to fully develop his evident talent.
Redknapp, whose autobiography has been serialised by the Daily Mail this week wrote: "He (Bale) drove me mad in training. 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'. He was always getting a little knock in training, too. He'd go down then limp off and I always thought the physios made too much fuss of him.
"It was the same pattern every morning - Gareth would tumble and stay there, and they'd all go running over. [I told them] 'If it is anything urgent we'll soon know'. That's what they did and, as predicted, Gareth got up, got on with it and got better and better."
Bale was recently voted the Welsh Player of the Year for the third time.