Gibson's decision paid off Wednesday night, as Bell worked around a leadoff double before closing the D-backs' 3-2 win over the Dodgers for his third save of the season.
"I just think Heath's got more experience at closer right now, and if we move Heath and David right now we're really moving the whole bullpen," Gibson said. "It just seems like it's less disruptive."
It is not known yet how long Putz is expected to be out.
Bell was the Padres' primary closer from 2009-11 and started 2012 as the Marlins' closer before losing that spot. The right-hander has saved 155 games in his career.
"It's something like riding a bike," said Bell, who is 2-0 with a 4.40 ERA 14 1/3 innings this season. "I've done it for the last four years."
After tremendous success in San Diego, Bell struggled during his season with the Marlins. After making some mechanical adjustments this year he feels like he has corrected his issues.
"I feel like I'm back to where I was back in San Diego," Bell said. "And I've got to give mad props to these guys for helping me get back there. I got back there a few weeks ago and I feel like the pitcher of old and I feel like I can go out there and give it all I have and rack up saves or rack up holds whatever they need."
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.