Redknapp was Bonds' assistant at West Ham and then took over from him when Bonds resigned in 1994.
In his book Redknapp said Bonds was "a man out of time" and presiding over a "shambles" when he left the club.
According to Redknapp, Bonds left the club after being unhappy at being offered a 10-year-contract to move upstairs as director of football, with the Hammers then offering Redknapp the top job to ward off interest from Bournemouth.
"For him to come out with what he said was disrespectful to the players and one or two of the staff who who were over there," Bonds said in an interview for West Ham website Knees Up Mother Brown to be published in full on Tuesday, extracts of which appear in the Mirror.
"I think he has been very liberal with the truth - but that's much as I expected really.
"I haven't spoken to him for 20 years. I find it quite pathetic that he comes out with stuff like that, really, to be honest with you."
Bonds played almost 800 games as a player for West Ham and was at the club as a player or coach for 27 years until he finally left.