Bertrand has already won an England cap and played in Chelsea's Champions League success last May, but the 23-year-old still has some improving to do to match Cole's standards.
Cole told Chelsea TV: "I didn't just sign because I wanted to play. There is a great player in Ryan and hopefully I can help him. If he gets more starts it will be good for the club to have two left backs here.
"I think it helps (having experienced players around the young players). I like to think I have helped Ryan in more ways than one.
"He deserves to be at a big club, he has improved a lot in the few years I've seen him and this year and next year is a chance for him to start more games.
"If I can stay here and help, it's good enough for me."