The left-back was signed by Mark Hughes for the Sky Blues for £12m, but Bridge has revealed he didn't think he was worth the amount.
Manchester City spent more than £100m on three new full-backs this summer, bringing in Kyle Walker, Benjamin Mendy and Danilo.
Yet when Bridge joined the club in January 2009, as one of the first arrivals of the Sheikh Mansour era, he felt transfer fees were already beginning to get out of hand.
“Even I pinch myself at the career I had and the money you can earn, but I almost find it embarrassing to talk about,” the 37-year-old said.
“When I was going for £12m to Man City I remember speaking to Jamie Redknapp about the price, and saying, ‘I think they’re paying too much.’
“He was like, ‘nah, you’re quality,’ but I didn’t see it.
“But the prices you’re talking about these days for full-backs, £50m, I can’t get my head round it.
"I never would have thought it would keep going up and up and up and up, but it’s still going.
"You think ‘when is it going to stop?’ and I really don’t know.”
Speaking on his spell at Chelsea which began in 2003 just after Roman Abramovich acquired the club, Bridge said he felt more relaxed about his £7m transfer fee.
“When there’s a group of you, you don’t feel as much pressure,” he added.
“I think if there’s just one or two there’s more of a spotlight on how you’re going to do, but it takes a bit of pressure off you personally.”
Bridge represented England on 34 occasions and scored once against Iceland.
