The third Ashes Test starts at Edgbaston on Wednesday with the five-match series level at 1-1.
Bell scored one and 11 during the Lord???s match which took his tally for the series to 73 runs in four innings.
But McCullum has backed the 33-year-old Warwickshire player to succeed in his new role, after being promoted up the order from four to three.
The New Zealand skipper said in his Daily Mail column: “I have said before that I felt Joe Root should be England’s No 3 but Ian Bell is the next best option.
“He’s a classy batsman who’s been there, done it and got the T-shirt: 112 Tests and 22 hundreds are figures we’d all love. I firmly believe it will work well for him.
“The challenge of moving up a place to No 3, where he has hardly batted at all in the past couple of years, should reinvigorate him. It will give him a chance to dictate play, not react to it.”
“I know Bell hasn’t scored the runs he’d have liked in recent Tests but you have to be very sure that the guy you’re bringing in to replace him is ready to go and up to the task.
“Whenever New Zealand have played against England, we have always regarded him as a very big wicket and I’m sure the Australians feel the same ??? especially after the three hundreds he got against them in the 2013 series.???