The Right Reverend Graham Tomlin said residents should be at the heart of the investigation, which is believed to have killed at least 80 people.
"If you keep... the people directly affected by it out of the inquiry process, it just takes an awful lot longer to get to the truth," he said.
Dr Tomlin, whose diocese includes the tower, said local trust was important.
His remarks were mirrored in his formal submission to the public consultation, which closed on Friday.
It is believed more than 300 submissions were made before the deadline.
Inquiry chairman Sir Martin Moore-Bick, a retired Court of Appeal judge, has already faced calls to resign from some residents of the west London tower block.
"It seems to me that the inquiry needs to get to the truth... but it also needs to win the confidence of the local people," Dr Tomlin told the BBC.
If it does not, he said, "whatever recommendations it makes is unlikely to get support."
He said the inquiry needs to not only look at the technical causes of the fire on the night in question, but also the issues faced by the community in the run-up to the tragedy.
"I want to see local people at the heart of the inquiry, not just on the outside," he said.
Residents' group Justice 4 Grenfell also made several submissions to the consultation process, including calling for investigation of the local council and a number of  government departments.
The fire in the 24-storey block started in a fridge freezer and destroyed 151 homes, both in the tower and surrounding areas.
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The Bishop of Kensington has called for locals to be closely involved in the Grenfell Tower fire inquiry.