Pope held off competition from Bethell for the number-three spot, although Bethell also offers the option of his left-arm spin.
Bashir has taken eight wickets in the India series, more than any other England bowler except Josh Tongue. However, the 21-year-old has been expensive – his wickets have cost almost 60 runs each and his economy is just below four an over.
However, McCullum said England will not “crowbar” Bethell into the team.
“He’s a batting option,” added the coach. “He’s the next one in if something happens.
“He wants to keep improving his bowling so that he can obviously impact the game across both the bat and ball. It’s not something we’d look at from a tactical point of view to do.”
One player set to be included in the England XI for the third Test at Lord’s, beginning on Thursday, is Jofra Archer.
The pace bowler, 30, has not played Test cricket in four years after a string of injuries, but seems likely to return as the home side freshen up their attack.
And McCullum said Archer is “certainly” available, despite bowling only 18 overs on his first-class comeback for Sussex last week.
“Jofra is looking fit, he’s looking strong, he’s looking ready to go, and he’ll come into calculations,” he added.
“It’s hugely exciting. He’s buzzing as well. He’s obviously been through his injuries and his time out of Test cricket.
“We all know what he’s capable of achieving in Test cricket and we hope that when the opportunity does arrive for him, he’s able to recapture and also improve on what he’s been able to do already in that form of the game.”