O'Driscoll succeeded Derek McInnes at Ashton Gate in January, with the club eight points adrift of safety. The former Nottingham Forest boss has since guided the Robins to five wins and two draws from his 11 games in charge.
City are now two points away from 21st-placed Barnsley and Heaton believes that O'Driscoll's methods have had an impact upon the players.
"It's amazing what a new face with a few new ideas can do to a club," BBC Sport quotes him as saying.
"We've been excellent since the new manager's come in. I think the potential we showed at the start of the season is coming into fruition.
"We're on a good run and hopefully we can keep it going to avoid relegation."
City face relegation rivals Wolverhampton Wanderers on Saturday.